Transmitting apparatus and interleaving method thereof

ABSTRACT

A television (TV) broadcasting signal transmitting apparatus includes least one processor configured to: interleave parity bits generated by encoding input bits based on a low density parity check (LDPC) code of which a code rate is 6/15 and a code length is 64800 bits; split a codeword comprising the input bits and the interleaved parity bits into a plurality of bit groups; interleave the plurality of bit groups based on an interleaving order to provide an interleaved codeword; de-multiplex bits of the interleaved codeword to generate data cells; map the data cells onto constellation points for 1024-quadrature amplitude modulation (QAM); and generate the TV broadcasting signal based on the mapped constellation points using orthogonal frequency division (OFDM) processing. The apparatus further includes a transmitter configured to transmit the generated TV broadcasting signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. application Ser. No. 16/925,368 filed Jul. 10, 2020, which is a continuation of U.S. application Ser. No. 16/352,142 filed Mar. 13, 2019, which is a continuation of U.S. application Ser. No. 15/609,707 filed May 31, 2017 (now U.S. Pat. No. 10,270,467), which is a continuation of U.S. application Ser. No. 14/662,379 filed Mar. 19, 2015 (now U.S. Pat. No. 9,685,980), which claims priority from U.S. Provisional Application No. 61/955,410 filed on Mar. 19, 2014, and Korean Patent Application No. 10-2015-0000677 filed on Jan. 5, 2015, the disclosures of which are incorporated herein by reference in their entirety.

BACKGROUND 1. Field

Apparatuses and methods consistent with exemplary embodiments relate to a transmitting apparatus and an interleaving method thereof, and more particularly, to a transmitting apparatus which processes and transmits data, and an interleaving method thereof.

2. Description of the Related Art

In the 21st century information-oriented society, broadcasting communication services are moving into an era of digitalization, multi-channel, wideband, and high quality. In particular, as higher quality digital televisions, portable multimedia players (PMPs) and portable broadcasting equipment are increasingly used in recent years, there is an increasing demand for methods for supporting various receiving methods of digital broadcasting services.

In order to meet such demand, standard groups are establishing various standards and are providing a variety of services to satisfy users' needs. Therefore, there is a need for a method for providing improved services to users with more robust encoding, decoding and receiving performance.

SUMMARY

One or more exemplary embodiments may overcome the above disadvantages and other disadvantages not described above. However, it is understood that one or more exemplary embodiment are not required to overcome the disadvantages described above, and may not overcome any of the problems described above.

One or more exemplary embodiments provide a transmitting apparatus which can map a bit included in a predetermined group from among a plurality of groups of a Low Density Parity Check (LDPC) codeword onto a predetermined bit of a modulation symbol, and transmit the bit, and an interleaving method thereof.

According to an aspect of an exemplary embodiment, there is provided a transmitting apparatus which may include: an encoder configured to generate an LDPC codeword by LDPC encoding based on a parity check matrix; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a plurality of modulation symbols, wherein the modulator is configured to map bits included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of each of the modulation symbols.

Each of the plurality of bit groups may be formed of M number of bits, and M may be a common divisor of N_(ldpc) and K_(ldpc) and determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) may be a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, N_(ldpc) may be a length of the LDPC codeword, and K_(ldpc) may be a length of information word bits of the LDPC codeword.

The interleaver may include: a parity interleaver configured to interleave parity bits of the LDPC codeword; a group interleaver configured to perform group interleaving on the parity-interleaved LDPC codeward by dividing the parity-interleaved LDPC codeword by the plurality of bit groups and rearranging an order of the plurality of bit groups in bits group wise; and a block interleaver configured to interleave the plurality of bit groups the order of which is rearranged.

The group interleaver may be configured to rearrange the order of the plurality of bit groups in bits group wise by using Equation 15.

In Equation 15, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 6/15, π(j) may be defined as in table 9.

When the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 8/15, π(j) may be defined as in table 10.

When the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 12/15, π(j) may be defined as in table 13:

The block interleaver may be configured to interleave by writing the plurality of bit groups in each of a plurality of columns in bits group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bits group wise in a row direction.

The block interleaver may be configured to serially write, in the plurality of columns, at least one bit group which is writable in the plurality of columns in bits group wise from among the plurality of bit groups, and divide and write bit groups other than the at least one bit group from among the plurality of bit groups in an area of the plurality of columns other than an area where the at least some bit group is written in the plurality of columns in bits group wise.

According to an aspect of another exemplary embodiment, there is provided an interleaving method of a transmitting apparatus which may include: generating an LDPC codeword by LDPC encoding based on a parity check matrix; interleaving the LDPC codeword; and mapping the interleaved LDPC codeword onto a plurality of modulation symbols, wherein the mapping comprises mapping bits included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of each of the modulation symbols.

Each of the plurality of bit groups may be formed of 360 bits, and M may be a common divisor of N_(ldpc) and K_(ldpc) and may be determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) may be a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, N_(ldpc) may be a length of the LDPC codeword, and K_(ldpc) may be a length of information word bits of the LDPC codeword.

The interleaving may include: interleaving parity bits of the LDPC codeword; group interleaving on the parity-interleaved LDPC codeward by dividing the parity-interleaved LDPC codeword by the plurality of bit groups and rearranging an order of the plurality of bit groups in bits group wise; and; and interleaving the plurality of bit groups the order of which is rearranged.

The rearranging in bits group wise may include rearranging the order of the plurality of bit groups in bits group wise by using Equation 15.

In Equation 15, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 6/15, π(j) may be defined as in table 9.

When the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 8/15, π(j) may be defined as in table 10.

When the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 12/15, π(j) may be defined as in table 13.

The interleaving the plurality of bit groups may include interleaving by writing the plurality of bit groups in each of a plurality of columns in bits group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bits group wise in a row direction.

The interleaving the plurality of bit groups may include: serially writing, in the plurality of columns, at least one bit group which is writable in the plurality of columns in bits group wise from among the plurality of bit groups; and dividing and writing bit groups other than the at least one bit group from among the plurality of bit groups in an area of the plurality of columns other than an area where the at least some bit group is written in the plurality of columns in bits group wise.

According to various exemplary embodiments as described above, improved decoding and receiving performance can be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describing in detail exemplary embodiments, with reference to the accompanying drawings, in which:

FIG. 1 is a block diagram to illustrate a configuration of a transmitting apparatus according to an exemplary embodiment;

FIGS. 2 and 3 are views to illustrate a configuration of a parity check matrix according to various exemplary embodiments;

FIG. 4 is a block diagram to illustrate a configuration of an interleaver according to an exemplary embodiment;

FIGS. 5 to 7 are views to illustrate a method for processing an LDPC codeword on a group basis according to exemplary embodiments;

FIGS. 8 to 12 are views to illustrate a configuration of a block interleaver and an interleaving method according to exemplary embodiments;

FIG. 13 is a view to illustrate an operation of a demultiplexer according to an exemplary embodiment;

FIG. 14 is a block diagram to illustrate a configuration of an interleaver according to another exemplary embodiment;

FIGS. 15-17 are views to illustrate a configuration of a block-row interleaver and an interleaving method according to exemplary embodiments;

FIG. 18 is a block diagram to illustrate a configuration of a receiving apparatus according to an exemplary embodiment;

FIGS. 19 and 21 are block diagrams to illustrate a configuration of a deinterleaver according to exemplary embodiments;

FIG. 20 is a view to illustrate a deinterleaving method of a block deinterleaver according to an exemplary embodiment; and

FIG. 22 is a flowchart to illustrate an interleaving method according to an exemplary embodiment.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Hereinafter, various exemplary embodiments will be described in greater detail with reference to the accompanying drawings.

In the following description, the same reference numerals are used for the same elements when they are depicted in different drawings. The matters defined in the description, such as detailed construction and elements, are provided to assist in a comprehensive understanding of the exemplary embodiments. Thus, it is apparent that the exemplary embodiments can be carried out without those specifically defined matters. Also, functions or elements known in the related art are not described in detail since they would obscure the exemplary embodiments with unnecessary detail.

FIG. 1 is a block diagram to illustrate a configuration of a transmitting apparatus according to an exemplary embodiment. Referring to FIG. 1, the transmitting apparatus 100 includes an encoder 110, an interleaver 120, and a modulator 130 (or a constellation mapper).

The encoder 110 generates a Low Density Parity Check (LDPC) codeword by performing LDPC encoding based on a parity check matrix. The encoder 110 may include an LDPC encoder (not shown) to perform the LDPC encoding.

Specifically, the encoder 110 LDPC-encodes information word (or information) bits to generate the LDPC codeword which is formed of the information word bits and parity bits (that is, LDPC parity bits). Here, bits input to the encoder 110 may be used as the information word bits. Also, since the LDPC code is a systematic code, the information word bits may be included in the LDPC codeword as they are.

The LDPC codeword is formed of the information word bits and the parity bits. For example, the LDPC codeword is formed of N_(ldpc) number of bits, and includes K_(ldpc) number of information word bits and N_(parity)=N_(ldpc)−K_(ldpc) number of parity bits.

In this case, the encoder 110 may generate the LDPC codeword by performing the LDPC encoding based on the parity check matrix. That is, since the LDPC encoding is a process for generating an LDPC codeword to satisfy H·C^(T)=0, the encoder 110 may use the parity check matrix when performing the LDPC encoding. Herein, H is a parity check matrix and C is an LDPC codeword.

For the LDPC encoding, the transmitting apparatus 100 may include a separate memory and may pre-store parity check matrices of various formats.

For example, the transmitting apparatus 100 may pre-store parity check matrices which are defined in Digital Video Broadcasting-Cable version 2 (DVB-C2), Digital Video Broadcasting-Satellite-Second Generation (DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial (DVB-T2), etc., or may pre-store parity check matrices which are defined in the North America digital broadcasting standard system Advanced Television System Committee (ATSC) 3.0 standards, which are currently being established. However, this is merely an example and the transmitting apparatus 100 may pre-store parity check matrices of other formats in addition to these parity check matrices.

Hereinafter, a parity check matrix according to various exemplary embodiments will be explained in detail with reference to the drawings. In the parity check matrix, elements other than elements with 1 have 0.

For example, the parity check matrix according to an exemplary embodiment may have the configuration of FIGS. 2 and 3.

Referring to FIG. 2, the parity check matrix 200 is formed of an information word submatrix (or information submatrix) 210 corresponding to information word bits, and a parity submatrix 220 corresponding to parity bits. In the parity check matrix 200, elements other than elements with 1 have 0.

The information word submatrix 210 includes K_(ldpc) number of columns and the parity submatrix 220 includes N_(parity)=N_(ldpc)−K_(ldpc) number of columns. The number of rows of the parity check matrix 200 is identical to the number of columns of the parity submatrix 220, N_(parity)=N_(ldpc)−K_(ldpc).

In addition, in the parity check matrix 200, N_(ldpc) is a length of an LDPC codeword, K_(ldpc) is a length of information word bits, and N_(parity)=N_(ldpc)−K_(ldpc) is a length of parity bits. The length of the LDPC codeword, the information word bits, and the parity bits mean the number of bits included in each of the LDPC codeword, the information word bits, and the parity bits.

Hereinafter, the configuration of the information word submatrix 210 and the parity submatrix 220 will be explained in detail.

The information word submatrix 210 includes K_(ldpc) number of columns (that is, 0^(th) column to (K_(ldpc)−1)^(th) column), and follows the following rules:

First, M number of columns from among K_(ldpc) number of columns of the information word submatrix 210 belong to a same group, and K_(ldpc) number of columns is divided into K_(ldpc)/M number of column groups. In each column group, a column is cyclic-shifted from an immediately previous column by Q_(ldpc) or Q_(ldpc) number of bits. That is, Q_(ldpc) may be a cyclic shift parameter value regarding columns in a column group of the information word submatrix 210 of the parity check matrix 200.

Herein, M is an interval at which a pattern of a column group, which includes a plurality of columns, is repeated in the information word submatrix 210 (e.g., M=360), and Q_(ldpc) is a size by which one column is cyclic-shifted from an immediately previous column in a same column group in the information word submatrix 210. Also, M is a common divisor of N_(ldpc) and K_(ldpc) and is determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Here, M and Q_(ldpc) are integers and K_(ldpc)/M is also an integer. M and Q_(ldpc) may have various values according to the length of the LDPC codeword and a code rate (CR) or a coding rate.

For example, when M=360 and the length of the LDPC codeword, N_(ldpc), is 64800, Q_(ldpc) may be defined as in Table 1 presented below, and, when M=360 and the length N_(ldpc) of the LDPC codeword is 16200, Q_(ldpc) may be defined as in Table 2 presented below.

TABLE 1 Code Rate N_(ldpc) M Q_(ldpc) 5/15 64800 360 120 6/15 64800 360 108 7/15 64800 360 96 8/15 64800 360 84 9/15 64800 360 72 10/15  64800 360 60 11/15  64800 360 48 12/15  64800 360 36 13/15  64800 360 24

TABLE 2 Code Rate N_(ldpc) M Q_(ldpc) 5/15 16200 360 30 6/15 16200 360 27 7/15 16200 360 24 8/15 16200 360 21 9/15 16200 360 18 10/15  16200 360 15 11/15  16200 360 12 12/15  16200 360 9 13/15  16200 360 6

Second, when the degree of the 0^(th) column of the i^(th) column group (i=0, 1, . . . , K_(ldpc)/M−1) is D_(i) (herein, the degree is the number of value 1 existing in each column and all columns belonging to the same column group have the same degree), and a position (or an index) of each row where 1 exists in the 0^(th) column of the i^(th) column group is R_(i,0) ⁽⁰⁾; R_(i,0) ⁽¹⁾, . . . , R_(i,0) ^((D) ^(i) ⁻¹⁾, an index R_(i,j) ^((k)) of a row where k^(th) 1 is located in the j^(th) column in the i^(th) column group is determined by following Equation 1:

R _(i,j) ^((k)) =R _(i,(j−1)) ^((k))Q_(ldpc) mod(N _(ldpc) −K _(ldpc))  (1),

where k=0, 1, 2, . . . D_(i)−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1, 2, . . . , M−1.

Equation 1 can be expressed as following Equation 2:

R _(i,j) ^((k)) ={R _(i,0) ^((k))+(j mod M)×Q _(ldpc)} mod(N _(ldpc) −K _(ldpc))  (2),

where k=0, 1, 2, . . . D_(i)−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1, 2, . . . , M−1. Since j=1, 2, . . . , M−1, (j mod M) of Equation 2 may be regarded as j.

In the above equations, R_(i,j) ^((k)) is an index of a row where k^(th) 1 is located in the j^(th) column in the i^(th) column group, N_(ldpc) is a length of an LDPC codeword, K_(ldpc) is a length of information word bits, D_(i) is a degree of columns belonging to the i^(th) column group, M is the number of columns belonging to a single column group, and Q_(ldpc) is a size by which each column in the column group is cyclic-shifted.

As a result, referring to these equations, when only R_(i,0) ^((k)) is known, the index R_(i,j) ^((k)) of the row where the k^(th) 1 is located in the j^(th) column in the i^(th) column group can be known. Therefore, when the index value of the row where the k^(th) 1 is located in the 0^(th) column of each column group is stored, a position of column and row where 1 is located in the parity check matrix 200 having the configuration of FIG. 2 (that is, in the information word submatrix 210 of the parity check matrix 200) can be known.

According to the above-described rules, all of the columns belonging to the i^(th) column group have the same degree D_(i). Accordingly, the LDPC codeword which stores information on the parity check matrix according to the above-described rules may be briefly expressed as follows.

For example, when N_(ldpc) is 30, K_(ldpc) is 15, and Q_(ldpc) is 3, position information of the row where 1 is located in the 0^(th) column of the three column groups may be expressed by a sequence of Equations 3 and may be referred to as “weight-1 position sequence”.

R _(1,0) ⁽¹⁾=1,R _(1,0) ⁽²⁾=2,R _(1,0) ⁽³⁾=8,R _(1,0) ⁽⁴⁾=10,

R _(2,0) ⁽¹⁾=0,R _(2,0) ⁽²⁾=9,R _(2,0) ⁽³⁾=13,

R _(3,0) ⁽¹⁾=0,R _(3,0) ⁽²⁾=14.  (3),

where R_(i,j) ^((k)) is an index of a row where k^(th) 1 is located in the j^(th) column in the i^(th) column group.

The weight-1 position sequence like Equation 3 which expresses an index of a row where 1 is located in the 0^(th) column of each column group may be briefly expressed as in Table 3 presented below:

TABLE 3 1 2 8 10 0 9 13 0 14

Table 3 shows positions of elements having value 1 in the parity check matrix, and the i^(th) weight-1 position sequence is expressed by indexes of rows where 1 is located in the 0^(th) column belonging to the i^(th) column group.

The information word submatrix 210 of the parity check matrix according to an exemplary embodiment may be defined as in Tables 4 to 8 presented below, based on the above descriptions.

Specifically, Tables 4 to 8 show indexes of rows where 1 is located in the 0th column of the i^(th) column group of the information word submatrix 210. That is, the information word submatrix 210 is formed of a plurality of column groups each including M number of columns, and positions of 1 in the 0^(th) column of each of the plurality of column groups may be defined by Tables 4 to 8.

Herein, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group mean “addresses of parity bit accumulators”. The “addresses of parity bit accumulators” have the same meaning as defined in the DVB-C2/S2/T2 standards or the ATSC 3.0 standards which are currently being established, and thus, a detailed explanation thereof is omitted.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 4 presented below:

TABLE 4 0 1606 3402 4961 6751 7132 11516 12300 12482 12592 13342 13764 14123 21576 23946 24533 25376 25667 26836 31799 34173 35462 36153 36740 37085 37152 37468 37658 1 4621 5007 6910 8732 9757 11508 13099 15513 16335 18052 19512 21319 23663 25628 27208 31333 32219 33003 33239 33447 36200 36473 36938 37201 37283 37495 38642 2 16 1094 2020 3080 4194 5098 5631 6877 7889 8237 9804 10067 11017 11366 13136 13354 15379 18934 20199 24522 26172 28666 30386 32714 36390 37015 37162 3 700 897 1708 6017 6490 7372 7825 9546 10398 16605 18561 18745 21625 22137 23693 24340 24966 25015 26995 28586 28895 29687 33938 34520 34858 37056 38297 4 159 2010 2573 3617 4452 4958 5556 5832 6481 8227 9924 10836 14954 15594 16623 18065 19249 22394 22677 23408 23731 24076 24776 27007 28222 30343 38371 5 3118 3545 4768 4992 5227 6732 8170 9397 10522 11508 15536 20218 21921 28599 29445 29758 29968 31014 32027 33685 34378 35867 36323 36728 36870 38335 38623 6 1264 4254 6936 9165 9486 9950 10861 11653 13697 13961 15164 15665 18444 19470 20313 21189 24371 26431 26999 28086 28251 29261 31981 34015 35850 36129 37186 7 111 1307 1628 2041 2524 5358 7988 8191 10322 11905 12919 14127 15515 15711 17061 19024 21195 22902 23727 24401 24608 25111 25228 27338 35398 37794 38196 8 961 3035 7174 7948 13355 13607 14971 18189 18339 18665 18875 19142 20615 21136 21309 21758 23366 24745 25849 25962 27583 30006 31118 32106 36469 36583 37920 9 2990 3549 4273 4808 5707 6021 6509 7456 8240 10044 12262 12660 13085 14750 15680 16049 21587 23997 25803 28343 28693 34393 34860 35490 36021 37737 38296 10 955 4323 5145 6885 8123 9730 11840 12216 19194 20313 23056 24248 24830 25268 26617 26801 28557 29753 30745 31450 31973 32839 33025 33296 35710 37366 37509 11 264 605 4181 4483 5156 7238 8863 10939 11251 12964 16254 17511 20017 22395 22818 23261 23422 24064 26329 27723 28186 30434 31956 33971 34372 36764 38123 12 520 2562 2794 3528 3860 4402 5676 6963 8655 9018 9783 11933 16336 17193 17320 19035 20606 23579 23769 24123 24966 27866 32457 34011 34499 36620 37526 13 10106 10637 10906 34242 14 1856 15100 19378 21848 15 943 11191 27806 29411 16 4575 6359 13629 19383 17 4476 4953 18782 24313 18 5441 6381 21840 35943 19 9638 9763 12546 30120 20 9587 10626 11047 25700 21 4088 15298 28768 35047 22 2332 6363 8782 28863 23 4625 4933 28298 30289 24 3541 4918 18257 31746 25 1221 25233 26757 34892 26 8150 16677 27934 30021 27 8500 25016 33043 38070 28 7374 10207 16189 35811 29 611 18480 20064 38261 30 25416 27352 36089 38469 31 1667 17614 25839 32776 32 4118 12481 21912 37945 33 5573 13222 23619 31271 34 18271 26251 27182 30587 35 14690 26430 26799 34355 36 13688 16040 20716 34558 37 2740 14957 23436 32540 38 3491 14365 14681 36858 39 4796 6238 25203 27854 40 1731 12816 17344 26025 41 19182 21662 23742 27872 42 6502 13641 17509 34713 43 12246 12372 16746 27452 44 1589 21528 30621 34003 45 12328 20515 30651 31432 46 3415 22656 23427 36395 47 632 5209 25958 31085 48 619 3690 19648 37778 49 9528 13581 26965 36447 50 2147 26249 26968 28776 51 15698 18209 30683 52 1132 19888 34111 53 4608 25513 38874 54 475 1729 34100 55 7348 32277 38587 56 182 16473 33082 57 3865 9678 21265 58 4447 20151 27618 59 6335 14371 38711 60 704 9695 28858 61 4856 9757 30546 62 1993 19361 30732 63 756 28000 29138 64 3821 24076 31813 65 4611 12326 32291 66 7628 21515 34995 67 1246 13294 30068 68 6466 33233 35865 69 14484 23274 38150 70 21269 36411 37450 71 23129 26195 37653

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 5 presented below:

TABLE 5 i Index of row where 1 is located in the 0th column of the ith column group 0 2768 3039 4059 5856 6245 7013 8157 9341 9802 10470 11521 12083 16610 18361 20321 24601 27420 28206 29788 1 2739 8244 8891 9157 12624 12973 15534 16622 16919 18402 18780 19854 20220 20543 22306 25540 27478 27678 28053 2 1727 2268 6246 7815 9010 9556 10134 10472 11389 14599 15719 16204 17342 17666 18850 22058 25579 25860 29207 3 28 1346 3721 5565 7019 9240 12355 13109 14800 16040 16839 17369 17631 19357 19473 19891 20381 23911 29683 4 869 2450 4386 5316 6160 7107 10362 11132 11271 13149 16397 16532 17113 19894 22043 22784 27383 28615 28804 5 508 4292 5831 8559 10044 10412 11283 14810 15888 17243 17538 19903 20528 22090 22652 27235 27384 28208 28485 6 389 2248 5840 6043 7000 9054 11075 11760 12217 12565 13587 15403 19422 19528 21493 25142 27777 28566 28702 7 1015 2002 5764 6777 9346 9629 11039 11153 12690 13068 13990 16841 17702 20021 24106 26300 29332 30081 30196 8 1480 3084 3467 4401 4798 5187 7851 11368 12323 14325 14546 16360 17158 18010 21333 25612 26556 26906 27005 9 6925 8876 12392 14529 15253 15437 19226 19950 20321 23021 23651 24393 24653 26668 27205 28269 28529 29041 29292 10 2547 3404 3538 4666 5126 5468 7695 8799 14732 15072 15881 17410 18971 19609 19717 22150 24941 27908 29018 11 888 1581 2311 5511 7218 9107 10454 12252 13662 15714 15894 17025 18671 24304 25316 25556 28489 28977 29212 12 1047 1494 1718 4645 5030 6811 7868 8146 10611 15767 17682 18391 22614 23021 23763 25478 26491 29088 29757 13 59 1781 1900 3814 4121 8044 8906 9175 11156 14841 15789 16033 16755 17292 18550 19310 22505 29567 29850 14 1952 3057 4399 9476 10171 10769 11335 11569 15002 19501 20621 22642 23452 24360 25109 25290 25828 28505 29122 15 2895 3070 3437 4764 4905 6670 9244 11845 13352 13573 13975 14600 15871 17996 19672 20079 20579 25327 27958 16 612 1528 2004 4244 4599 4926 5843 7684 10122 10443 12267 14368 18413 19058 22985 24257 26202 26596 27899 17 1361 2195 4146 6708 7158 7538 9138 9998 14862 15359 16076 18925 21401 21573 22503 24146 24247 27778 29312 18 5229 6235 7134 7655 9139 13527 15408 16058 16705 18320 19909 20901 22238 22437 23654 25131 27550 28247 29903 19 697 2035 4887 5275 6909 9166 11805 15338 16381 18403 20425 20688 21547 24590 25171 26726 28348 29224 29412 20 5379 17329 22659 23062 21 11814 14759 22329 22936 22 2423 2811 10296 12727 23 8460 15260 16769 17290 24 14191 14608 29536 30187 25 7103 10069 20111 22850 26 4285 15413 26448 29069 27 548 2137 9189 10928 28 4581 7077 23382 23949 29 3942 17248 19486 27922 30 8668 10230 16922 26678 31 6158 9980 13788 28198 32 12422 16076 24206 29887 33 8778 10649 18747 22111 34 21029 22677 27150 28980 35 7918 15423 27672 27803 36 5927 18086 23525 37 3397 15058 30224 38 24016 25880 26268 39 1096 4775 7912 40 3259 17301 20802 41 129 8396 15132 42 17825 28119 28676 43 2343 8382 28840 44 3907 18374 20939 45 1132 1290 8786 46 1481 4710 28846 47 2185 3705 26834 48 5496 15681 21854 49 12697 13407 22178 50 12788 21227 22894 51 629 2854 6232 52 2289 18227 27458 53 7593 21935 23001 54 3836 7081 12282 55 7925 18440 23135 56 497 6342 9717 57 11199 22046 30067 58 12572 28045 28990 59 1240 2023 10933 60 19566 20629 25186 61 6442 13303 28813 62 4765 10572 16180 63 552 19301 24286 64 6782 18480 21383 65 11267 12288 15758 66 771 5652 15531 67 16131 20047 25649 68 13227 23035 24450 69 4839 13467 27488 70 2852 4677 22993 71 2504 28116 29524 72 12518 17374 24267 73 1222 11859 27922 74 9660 17286 18261 75 232 11296 29978 76 9750 11165 16295 77 4894 9505 23622 78 10861 11980 14110 79 2128 15883 22836 80 6274 17243 21989 81 10866 13202 22517 82 11159 16111 21608 83 3719 18787 22100 84 1756 2020 23901 85 20913 29473 30103 86 2729 15091 26976 87 4410 8217 12963 88 5395 24564 28235 89 3859 17909 23051 90 5733 26005 29797 91 1935 3492 29773 92 11903 21380 29914 93 6091 10469 29997 94 2895 8930 15594 95 1827 10028 20070

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and M is 360, the indexes of rows where 1 exists in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are defined as shown in Table 6 or 7 below.

TABLE 6 i Index of row where 1 is located in the 0th column of the ith column group 0 979 1423 4166 4609 6341 8258 10334 10548 14098 14514 17051 17333 17653 17830 17990 1 2559 4025 6344 6510 9167 9728 11312 14856 17104 17721 18600 18791 19079 19697 19840 2 3243 6894 7950 10539 12042 13233 13938 14752 16449 16727 17025 18297 18796 19400 21577 3 3272 3574 6341 6722 9191 10807 10957 12531 14036 15580 16651 17007 17309 19415 19845 4 155 4598 10201 10975 11086 11296 12713 15364 15978 16395 17542 18164 18451 18612 20617 5 1128 1999 3926 4069 5558 6085 6337 8386 10693 12450 15438 16223 16370 17308 18634 6 2408 2929 3630 4357 5852 7329 8536 8695 10603 11003 14304 14937 15767 18402 21502 7 199 3066 6446 6849 8973 9536 10452 12857 13675 15913 16717 17654 19802 20115 21579 8 312 870 2095 2586 5517 6196 6757 7311 7368 13046 15384 18576 20349 21424 21587 9 985 1591 3248 359 3706 3847 6174 6276 7864 9033 13618 15675 16446 18355 18843 10 979 3774 4083 5825 6166 7218 7633 9657 10103 13052 14240 17320 18126 19544 20208 11 1795 2005 2544 3418 6148 8051 9066 9725 10676 10752 11512 15171 17523 20481 21059 12 167 315 1824 2325 2640 2868 6070 6597 7016 8109 9815 11608 16142 17912 19625 13 1298 1896 3039 4303 4690 8787 12241 13600 14478 15492 16602 17115 17913 19466 20597 14 568 3695 6045 6624 8131 8404 8590 9059 9246 11570 14336 18657 18941 19218 21506 15 228 1889 1967 2299 3011 5074 7044 7596 7689 9534 10244 10697 11691 17902 21410 16 1330 1579 1739 2234 3701 3865 5713 6677 7263 11172 12143 12765 17121 20011 21436 17 303 1668 2501 4925 5778 5985 9635 10140 10820 11779 11849 12058 15650 20426 20527 18 698 2484 3071 3219 4054 4125 5663 5939 6928 7086 8054 12173 16280 17945 19302 19 232 1619 3040 4901 7438 8135 9117 9233 10131 13321 17347 17436 18193 18586 19929 20 12 3721 6254 6609 7880 8139 10437 12262 13928 14065 14149 15032 15694 16264 18883 21 482 915 1548 1637 6687 9338 10163 11768 11970 15524 15695 17386 18787 19210 19340 22 1291 2500 4109 4511 5099 5194 10014 13165 13256 13972 15409 16113 16214 18584 20998 23 1761 4778 7444 7740 8129 8341 8931 9136 9207 10003 10678 13959 17673 18194 20990 24 3060 3522 5361 5692 6833 8342 8792 11023 11211 11548 11914 13987 15442 15541 19707 25 1322 2348 2970 5632 6349 7577 8782 9113 9267 9376 12042 12943 16680 16970 21321 26 6785 11960 21455 27 1223 15672 19550 28 5976 11335 20385 29 2818 9387 15317 30 2763 3554 18102 31 5230 11489 18997 32 5809 15779 20674 33 2620 17838 18533 34 3025 9342 9931 35 3728 5337 12142 36 2520 6666 9164 37 12892 15307 20912 38 10736 12393 16539 39 1075 2407 12853 40 4921 5411 18206 41 5955 15647 16838 42 6384 10336 19266 43 429 10421 17266 44 4880 10431 12208 45 2910 11895 12442 46 7366 18362 18772 47 4341 7903 14994 48 4564 6714 7378 49 4639 8652 18871 50 15787 18048 20246 51 3241 11079 13640 52 1559 2936 15881 53 2737 6349 10881 54 10394 16107 17073 55 8207 9043 12874 56 7805 16058 17905 57 11189 15767 17764 58 5823 12923 14316 59 11080 20390 20924 60 568 8263 17411 61 1845 3557 6562 62 2890 10936 14756 63 9031 14220 21517 64 3529 12955 15902 65 413 6750 8735 66 6784 12092 16421 67 12019 13794 15308 68 12588 15378 17676 69 8067 14589 19304 70 1244 5877 6085 71 15897 19349 19993 72 1426 2394 12264 73 3456 8931 12075 74 13342 15273 20351 75 9138 13352 20798 76 7031 7626 14081 77 4280 4507 15617 78 4170 10569 14335 79 3839 7514 16578 80 4688 12815 18782 81 4861 7858 9435 82 605 5445 12912 83 2280 4734 7311 84 6668 8128 12638 85 3733 10621 19534 86 13933 18316 19341 87 1786 3037 21566 88 2202 13239 16432 89 4882 5808 9300 90 4580 8484 16754 91 14630 17502 18269 92 6889 11119 12447 93 8162 9078 16330 94 6538 17851 18100 95 17763 19793 20816 96 2183 11907 17567 97 6640 14428 15175 98 877 12035 14081 99 1336 6468 12328 100 5948 9146 12003 101 3782 5699 12445 102 1770 7946 8244 103 7384 12639 14989 104 1469 11586 20959 105 7943 10450 15907 106 5005 8153 10035 107 17750 18826 21513 108 4725 8041 10112 109 3837 16266 17376 110 11340 17361 17512 111 1269 4611 4774 112 2322 10813 16157 113 16752 16843 18959 114 70 4325 18753 115 3165 8153 15384 116 160 8045 16823 117 14112 16724 16792 118 4291 7667 18176 119 5943 19879 20721

TABLE 7 i Index of row where 1 is located in the 0th column of the ith column group 0 316 1271 3692 9495 12147 12849 14928 16671 16938 17864 19108 20502 21097 21115 1 2341 2559 2643 2816 2865 5137 5331 7000 7523 8023 10439 10797 13208 15041 2 5556 6858 7677 10162 10207 11349 12321 12398 14787 15743 15859 15952 19313 20879 3 349 573 910 2702 3654 6214 9246 9353 10638 11772 14447 14953 16620 19888 4 204 1390 2887 3835 6230 6533 7443 7876 9299 10291 10896 13960 18287 20086 5 541 2429 2838 7144 8523 8637 10490 10585 11074 12074 15762 16812 17900 18548 6 733 1659 3838 5323 5805 7882 9429 10682 13697 16909 18846 19587 19592 20904 7 1134 2136 4631 4653 4718 5197 10410 11666 14996 15305 16048 17417 18960 20303 8 734 1001 1283 4959 10016 10176 10973 11579 12051 15550 15915 19022 19430 20121 9 745 4057 5855 9885 10594 10989 13156 13219 13351 13631 13685 14577 17713 20386 10 968 1446 2130 2502 3092 3787 5323 8104 8418 9998 11681 13972 17747 17929 11 3020 3857 5275 5786 6319 8608 11943 14062 17144 17752 18001 18453 19311 21414 12 709 747 1038 2181 5320 8292 10584 10859 13964 15009 15277 16953 20675 21509 13 1663 3247 5003 5760 7186 7360 10346 14211 14717 14792 15155 16128 17355 17970 14 516 578 1914 6147 9419 11148 11434 13289 13325 13332 19106 19257 20962 21556 15 5009 5632 6531 9430 9886 10621 11765 13969 16178 16413 18110 18249 20616 20759 16 457 2686 3318 4608 5620 5858 6480 7430 9602 12691 14664 18777 20152 20848 17 33 2877 5334 6851 7907 8654 10688 15401 16123 17942 17969 18747 18931 20224 18 87 897 7636 8663 11425 12288 12672 14199 16435 17615 17950 18953 19667 20281 19 1042 1832 2545 2719 2947 3672 3700 6249 6398 6833 11114 14283 17694 20477 20 326 488 2662 2880 3009 5357 6587 8882 11604 14374 18781 19051 19057 20508 21 854 1294 2436 2852 4903 6466 7761 9072 9564 10321 13638 15658 16946 19119 22 194 899 1711 2408 2786 5391 7108 8079 8716 11453 17303 19484 20989 21389 23 1631 3121 3994 5005 7810 8850 10315 10589 13407 17162 18624 18758 19311 20301 24 736 2424 4792 5600 6370 10061 16053 16775 18600 25 1254 8163 8876 9157 12141 14587 16545 17175 18191 26 388 6641 8974 10607 10716 14477 16825 17191 18400 27 5578 6082 6824 7360 7745 8655 11402 11665 12428 28 3603 8729 13463 14698 15210 19112 19550 20727 21052 29 48 1732 3805 5158 15442 16909 19854 21071 21579 30 11707 14014 21531 31 1542 4133 4925 32 10083 13505 21198 33 14300 15765 16752 34 778 1237 11215 35 1325 3199 14534 36 2007 14510 20599 37 1996 5881 16429 38 5111 15018 15980 39 4989 10681 12810 40 3763 10715 16515 41 2259 10080 15642 42 9032 11319 21305 43 3915 15213 20884 44 11150 15022 20201 45 1147 6749 19625 46 12139 12939 18870 47 3840 4634 10244 48 1018 10231 17720 49 2708 13056 13393 50 5781 11588 18888 51 1345 2036 5252 52 5908 8143 15141 53 1804 13693 18640 54 10433 13965 16950 55 9568 10122 15945 56 547 6722 14015 57 321 12844 14095 58 2632 10513 14936 59 6369 11995 20321 60 9920 19136 21529 61 1990 2726 10183 62 5763 12118 15467 63 503 10006 19564 64 9839 11942 19472 65 11205 13552 15389 66 8841 13797 19697 67 124 6053 18224 68 6477 14406 21146 69 1224 8027 16011 70 3046 4422 17717 71 739 12308 17760 72 4014 4130 7835 73 2266 5652 11981 74 2711 7970 18317 75 2196 15229 17217 76 8636 13302 16764 77 5612 15010 16657 78 615 1249 4639 79 3821 12073 18506 80 1066 16522 21536 81 11307 18363 19740 82 3240 8560 10391 83 3124 11424 20779 84 1604 8861 17394 85 2083 7400 8093 86 3218 7454 9155 87 9855 15998 20533 88 316 2850 20652 89 5583 9768 10333 90 7147 7713 18339 91 12607 17428 21418 92 14216 16954 18164 93 8477 15970 18488 94 1632 8032 9751 95 4573 9080 13507 96 11747 12441 13876 97 1183 15605 16675 98 4408 10264 17109 99 5495 7882 12150 100 1010 3763 5065 101 9828 18054 21599 102 6342 7353 15358 103 6362 9462 19999 104 7184 13693 17622 105 4343 4654 10995 106 7099 8466 18520 107 11505 14395 15138 108 6779 16691 18726 109 7146 12644 20196 110 5865 16728 19634 111 4657 8714 21246 112 4580 5279 18750 113 3767 6620 18905 114 9209 13093 17575 115 12486 15875 19791 116 8046 14636 17491 117 2120 4643 13206 118 6186 9675 12601 119 784 5770 21585

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and M is 360, the indexes of rows where 1 exists in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are defined as shown in Table 8 below.

TABLE 8 i Index of row where 1 is located in the 0th column of the ith column group 0 584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632 8940 9725 1 221 445 590 3779 3835 6939 7743 8280 8448 8491 9367 10042 11242 12917 2 4662 4837 4900 5029 6449 6687 6751 8684 9936 11681 11811 11886 12089 12909 3 2418 3018 3647 4210 4473 7447 7502 9490 10067 11092 11139 11256 12201 12383 4 2591 2947 3349 3406 4417 4519 5176 6672 8498 8863 9201 11294 11376 12184 5 27 101 197 290 871 1727 3911 5411 6676 8701 9350 10310 10798 12439 6 1765 1897 2923 3584 3901 4048 6963 7054 7132 9165 10184 10824 11278 12669 7 2183 3740 4808 5217 5660 6375 6787 8219 8466 9037 10353 10583 11118 12762 8 73 1594 2146 2715 3501 3572 3639 3725 6959 7187 8406 10120 10507 10691 9 240 732 1215 2185 2788 2830 3499 3881 4197 4991 6425 7061 9756 10491 10 831 1568 1828 3424 4319 4516 4639 6018 9702 10203 10417 11240 11518 12458 11 2024 2970 3048 3638 3676 4152 5284 5779 5926 9426 9945 10873 11787 11837 12 1049 1218 1651 2328 3493 4363 5750 6483 7613 8782 9738 9803 11744 11937 13 1193 2060 2289 2964 3478 4592 4756 6709 7162 8231 8326 11140 11908 12243 14 978 2120 2439 3338 3850 4589 6567 8745 9656 9708 10161 10542 10711 12639 15 2403 2938 3117 3247 3711 5593 5844 5932 7801 10152 10226 11498 12162 12941 16 1781 2229 2276 2533 3582 3951 5279 5774 7930 9824 10920 11038 12340 12440 17 289 384 1980 2230 3464 3873 5958 8656 8942 9006 10175 11425 11745 12530 18 155 354 1090 1330 2002 2236 3559 3705 4922 5958 6576 8564 9972 12760 19 303 876 2059 2142 5244 5330 6644 7576 8614 9598 10410 10718 11033 12957 20 3449 3617 4408 4602 4727 6182 8835 8928 9372 9644 10237 10747 11655 12747 21 811 2565 2820 8677 8974 9632 11069 11548 11839 12107 12411 12695 12812 12890 22 972 4123 4943 6385 6449 7339 7477 8379 9177 9359 10074 11709 12552 12831 23 842 973 1541 2262 2905 5276 6758 7099 7894 8128 8325 8663 8875 10050 24 474 791 968 3902 4924 4965 5085 5908 6109 6329 7931 9038 9401 10568 25 1397 4461 4658 5911 6037 7127 7318 8678 8924 9000 9473 9602 10446 12692 26 1334 7571 12881 27 1393 1447 7972 28 633 1257 10597 29 4843 5102 11056 30 3294 8015 10513 31 1108 10374 10546 32 5353 7824 10111 33 3398 7674 8569 34 7719 9478 10503 35 2997 9418 9581 36 5777 6519 11229 37 1966 5214 9899 38 6 4088 5827 39 836 9248 9612 40 483 7229 7548 41 7865 8289 9804 42 2915 11098 11900 43 6180 7096 9481 44 1431 6786 8924 45 748 6757 8625 46 3312 4475 7204 47 1852 8958 11020 48 1915 2903 4006 49 6776 10886 12531 50 2594 9998 12742 51 159 2002 12079 52 853 3281 3762 53 5201 5798 6413 54 3882 6062 12047 55 4133 6775 9657 56 228 6874 11183 57 7433 10728 10864 58 7735 8073 12734 59 2844 4621 11779 60 3909 7103 12804 61 6002 9704 11060 62 5864 6856 7681 63 3652 5869 7605 64 2546 2657 4461 65 2423 4203 9111 66 244 1855 4691 67 1106 2178 6371 68 391 1617 10126 69 250 9259 10603 70 3435 4614 6924 71 1742 8045 9529 72 7667 8875 11451 73 4023 6108 6911 74 8621 10184 11650 75 6726 10861 12348 76 3228 6302 7388 77 1 1137 5358 78 381 2424 8537 79 3256 7508 10044 80 1980 2219 4569 81 2468 5699 10319 82 2803 3314 12808 83 8578 9642 11533 84 829 4585 7923 85 59 329 5575 86 1067 5709 6867 87 1175 4744 12219 88 109 2518 6756 89 2105 10626 11153 90 5192 10696 10749 91 6260 7641 8233 92 2998 3094 11214 93 3398 6466 11494 94 6574 10448 12160 95 2734 10755 12780 96 1028 7958 10825 97 8545 8602 10793 98 392 3398 11417 99 6639 9291 12571 100 1067 7919 8934 101 1064 2848 12753 102 6076 8656 12690 103 5504 6193 10171 104 1951 7156 7356 105 4389 4780 7889 106 526 4804 9141 107 1238 3648 10464 108 2587 5624 12557 109 5560 5903 11963 110 1134 2570 3297 111 10041 11583 12157 112 1263 9585 12912 113 3744 7898 10646 114 45 9074 10315 115 1051 6188 10038 116 2242 8394 12712 117 3598 9025 12651 118 2295 3540 5610 119 1914 4378 12423 120 1766 3635 12759 121 5177 9586 11143 122 943 3590 11649 123 4864 6905 10454 124 5852 6042 10421 125 6095 8285 12349 126 2070 7171 8563 127 718 12234 12716 128 512 10667 11353 129 3629 6485 7040 130 2880 8865 11466 131 4490 10220 11796 132 5440 8819 9103 133 5262 7543 12411 134 516 7779 10940 135 2515 5843 9202 136 4684 5994 10586 137 573 2270 3324 138 7870 8317 10322 139 6856 7638 12909 140 1583 7669 10781 141 8141 9085 12555 142 3903 5485 9992 143 4467 11998 12904

In the above-described examples, the length of the LDPC codeword is 64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, this is merely an example and the position of 1 in the information word submatrix 210 may be defined variously when the length of the LDPC codeword is 16200 or the code rate has different values.

According to an exemplary embodiment, even when an order of numbers, i.e., indexes, in a sequence corresponding to the i^(th) column group of the parity check matrix 200 as shown in the above-described Tables 4 to 8 is changed, the changed parity check matrix is a parity check matrix used for the same LDPC code. Therefore, a case in which the order of numbers in the sequence corresponding to the i^(th) column group in Tables 4 to 8 is changed is also covered by the present inventive concept.

In addition, even when an arrangement order of sequences corresponding to each column group shown in Tables 4 to 8 is changed, cycle characteristics on a graph of the LDPC code and algebraic characteristics such as degree distribution are not changed. Therefore, a case in which the arrangement order of the sequences shown in Tables 4 to 8 is changed is also covered by the present inventive concept.

In addition, even when a multiple of Q_(ldpc) is equally added to all sequences corresponding to a certain column group in Tables 4 to 8, the cycle characteristics on the graph of the LDPC code or the algebraic characteristics such as degree distribution are not changed. Therefore, a result of equally adding a multiple of Q_(ldpc) to the sequences shown in Tables 4 to 8 is also covered by the present inventive concept. However, it should be noted that, when the resulting value obtained by adding the multiple of Q_(ldpc) to a given sequence is greater than or equal to (N_(ldpc)−K_(ldpc)), a value obtained by applying a modulo operation for (N_(ldpc)−K_(ldpc)) to the resulting value should be applied instead.

Once positions of the rows where 1 exists in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are defined as shown in Tables 4 to 8, positions of rows where 1 exists in another column of each column group may be defined since the positions of the rows where 1 exists in the 0^(th) column are cyclic-shifted by Q_(ldpc) in the next column.

For example, in the case of Table 4, in the 0^(th) column of the 0^(th) column group of the information word submatrix 210, 1 exists in the 1606^(th) row, 3402^(nd) row, 4961^(st) row, . . . .

In this case, since Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M=(64800−25920)/360=108, the indexes of the rows where 1 is located in the 1^(st) column of the 0^(th) column group may be 1714=1606+108), 3510(=3402+108), 5069(=4961+108), . . . , and the indexes of the rows where 1 is located in the 2^(nd) column of the 0^(th) column group may be 1822(=1714+108), 3618(=3510+108), 5177(=5069+108) . . . .

In the above-described method, the indexes of the rows where 1 is located in all columns of each column group may be defined.

The parity submatrix 220 of the parity check matrix 200 shown in FIG. 2 may be defined as follows:

The parity submatrix 220 includes N_(ldpc)−K_(ldpc) number of columns (that is, K_(ldpc) ^(th) column to (N_(ldpc)−1)^(th) column), and has a dual diagonal or staircase configuration. Accordingly, the degree of columns except the last column (that is, (N_(ldpc)−1)^(th) column) from among the columns included in the parity submatrix 220 is 2, and the degree of the last column is 1.

As a result, the information word submatrix 210 of the parity check matrix 200 may be defined by Tables 4 to 8, and the parity submatrix 220 of the parity check matrix 200 may have a dual diagonal configuration.

When the columns and rows of the parity check matrix 200 shown in FIG. 2 are permutated based on Equation 4 and Equation 5, the parity check matrix shown in FIG. 2 may be changed to a parity check matrix 300 shown in FIG. 3.

Q _(ldpc) ·i+j=>j+i (0≤i<M,0≤j<Q _(ldpc))  (4)

K _(ldpc) +Q _(ldpc) ·k+l=>K _(ldpc) +M·l+k (0≤k<M,0≤1<Q _(ldpc))  (5)

The method for permutating based on Equation 4 and Equation 5 will be explained below. Since row permutation and column permutation apply the same principle, the row permutation will be explained by the way of an example.

In the case of the row permutation, regarding the X^(th) row, i and j satisfying X=Q_(ldpc)=i+j are calculated and the X^(th) row is permutated by assigning the calculated i and j to M×j+i. For example, regarding the 7^(th) row, i and j satisfying 7=2×i+j are 3 and 1, respectively. Therefore, the 7^(th) row is permutated to the 13^(th) row (10×1+3=13).

When the row permutation and the column permutation are performed in the above-described method, the parity check matrix of FIG. 2 may be converted into the parity check matrix of FIG. 3.

Referring to FIG. 3, the parity check matrix 300 is divided into a plurality of partial blocks, and a quasi-cyclic matrix of M×M corresponds to each partial block.

Accordingly, the parity check matrix 300 having the configuration of FIG. 3 is formed of matrix units of M×M. That is, the submatrices of M×M are arranged in the plurality of partial blocks, constituting the parity check matrix 300.

Since the parity check matrix 300 is formed of the quasi-cyclic matrices of M×M, M number of columns may be referred to as a column block and M number of rows may be referred to as a row block. Accordingly, the parity check matrix 300 having the configuration of FIG. 3 is formed of N_(qc_column)=N_(ldpc)/M number of column blocks and N_(qc_row)=N_(parity)/M number of row blocks.

Hereinafter, the submatrix of M×M will be explained.

First, the (N_(qc_column)−1)^(th) column block of the 0^(th) row block A 330 has the format of Equation 6 presented below:

$\begin{matrix} {A = \begin{bmatrix} 0 & 0 & \ldots & 0 & 0 \\ 1 & 0 & \ldots & 0 & 0 \\ 0 & 1 & \ldots & 0 & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & \ldots & 1 & 0 \end{bmatrix}} & (6) \end{matrix}$

As described above, A 330 is an M×M matrix, values of the 0^(th) row and the (M−1)^(th) column are all “0”, and, regarding 0≤i≤(M−2), the (i+1)^(th) row of the i^(th) column is “1” and the other values are “0”.

Second, regarding 0≤i≤(N_(ldpc)−K_(ldpc))/M−1 in the parity submatrix 320, the i^(th) row block of the (K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M) 340. In addition, regarding 0≤i≤(N_(ldpc)−K_(ldpc))/M−2, the (i+1)^(th) row block of the (K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M) 340.

Third, a block 350 constituting the information word submatrix 310 may have a cyclic-shifted format of a cyclic matrix P^(a) ^(ij) , or an added format of the cyclic-shifted matrix P^(a) ^(ij) of the cyclic matrix P (or an overlapping format).

For example, a format in which the cyclic matrix P is cyclic-shifted to the right by 1 may be expressed by Equation 7 presented below:

$\begin{matrix} {P = \begin{bmatrix} 0 & 1 & 0 & \; & 0 \\ 0 & 0 & 1 & \ldots & 0 \\ \vdots & \vdots & \vdots & \; & \vdots \\ 0 & 0 & 0 & \ldots & 1 \\ 1 & 0 & 0 & \; & 0 \end{bmatrix}} & (7) \end{matrix}$

The cyclic matrix P is a square matrix having an M×M size and is a matrix in which a weight of each of M number of rows is 1 and a weight of each of M number of columns is 1. When a_(ij) is 0, the cyclic matrix P, that is, P⁰ indicates a unit matrix I_(M×M), and when a_(ij) is ∞, P^(∞) is a zero matrix.

A submatrix existing where the i^(th) row block and the j^(th) column block intersect in the parity check matrix 300 of FIG. 3 may be P^(a) ^(ij) . Accordingly, i and j indicate the number of row blocks and the number of column blocks in the partial blocks corresponding to the information word. Accordingly, in the parity check matrix 300, the total number of columns is N_(ldpc)=M×N_(qc_column), and the total number of rows is N_(parity)=M×N_(qc_row). That is, the parity check matrix 300 is formed of N_(qc_column) number of “column blocks” and N_(qc_row) number of “row blocks”.

Hereinafter, a method for performing LDPC encoding based on the parity check matrix 200 as shown in FIG. 2 will be explained. An LDPC encoding process when the parity check matrix 200 is defined as shown in Table 4 by way of an example will be explained for the convenience of explanation.

First, when information word bits having the length of K_(ldpc) are [i₀, i₁, i₂, . . . , i_(L) _(ldpc) ⁻¹], and parity bits having the length of N_(ldpc)−K_(ldpc) are [p₀, p₁, p₂, . . . p_(N) _(ldpc) _(−K) _(ldpc) ⁻¹], the LDPC encoding is performed by the following process.

Step 1) Parity bits are initialized as ‘0’. That is, p₀=p₁=p₂= . . . =p_(N) _(ldpc) _(−K) _(ldpc) ⁻¹=0.

Step 2) The 0^(th) information word bit i₀ is accumulated in a parity bit having the address of the parity bit defined in the first row (that is, the row of i=0) of Table 4 as the index of the parity bit. This may be expressed by Equation 8 presented below:

P ₁₆₀₆ =P ₁₆₀₆ ⊕i ₀

P ₃₄₀₂ =P ₃₄₀₂ ⊕i ₀

P ₄₉₆₁ =P ₄₉₆₁ ⊕i ₀

P ₅₇₅₁ =P ₅₇₅₁ ⊕i ₀

P ₇₁₃₂ =P ₇₁₃₂ ⊕i ₀

P ₁₁₅₁₆ =P ₁₁₅₁₆ ⊕i ₀

P ₁₂₃₀₀ =P ₁₂₃₀₀ ⊕i ₀

P ₁₂₄₈₂ =P ₁₂₄₈₂ ⊕i ₀

P ₁₂₅₉₂ =P ₁₂₅₉₂ ⊕i ₀

P ₁₃₃₄₂ =P ₁₃₃₄₂ ⊕i ₀

P ₁₃₇₆₄ =P ₁₃₇₆₄ ⊕i ₀

P ₁₄₁₂₃ =P ₁₄₁₂₃ ⊕i ₀

P ₂₁₅₇₆ =P ₂₁₅₇₆ ⊕i ₀

P ₂₃₉₄₆ =P ₂₃₉₄₆ ⊕i ₀

P ₂₄₅₃₃ =P ₂₄₅₃₃ ⊕i ₀

P ₂₅₃₇₆ =P ₂₅₃₇₆ ⊕i ₀

P ₂₅₆₆₇ =P ₂₅₆₆₇ ⊕i ₀

P ₂₆₈₃₆ =P ₂₆₈₃₆ ⊕i ₀

P ₃₁₇₉₉ =P ₃₁₇₉₉ ⊕i ₀

P ₃₄₁₇₃ =P ₃₄₁₇₃ ⊕i ₀

P ₃₅₄₆₂ =P ₃₅₄₆₂ ⊕i ₀

P ₃₆₁₅₃ =P ₃₆₁₅₃ ⊕i ₀

P ₃₆₇₄₀ =P ₃₆₇₄₀ ⊕i ₀

P ₃₇₀₈₅ =P ₃₇₀₈₅ ⊕i ₀

P ₃₇₁₅₂ =P ₃₇₁₅₂ ⊕i ₀

P ₃₇₄₆₈ =P ₃₇₄₆₈ ⊕i ₀

P ₃₇₆₅₈ =P ₃₇₆₅₈ ⊕i ₀  (8)

Herein, i₀ is a 0^(th) information word bit, p_(i) is an i^(th) parity bit, and ⊕ is a binary operation. According to the binary operation, 1⊕1 equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 3) The other 359 information word bits i_(m) (m=1, 2, . . . , 359) are accumulated in the parity bit. The other information word bits may belong to the same column group as that of i₀. In this case, the address of the parity bit may be determined based on Equation 9 presented below:

(x+(m mod 360)×Q _(ldpc))mod(N _(ldpc) −K _(ldpc))  (9)

In the above, x is an address of a parity bit accumulator corresponding to the information word bit i₀, and Q_(ldpc) is a size by which each column is cyclic-shifted in the information word submatrix, and may be 108 in the case of Table 4. In addition, since m=1, 2, . . . , 359, (m mod 360) in Equation 9 may be regarded as m.

As a result, information word bits i_(m) (m=1, 2, . . . , 359) are accumulated in the parity bits having addresses of the parity bits calculated based on Equation 9 as the indexes, respectively. For example, an operation as shown in Equation 10 presented below may be performed for the information word bit i₁:

P ₁₇₁₄ =P ₁₇₁₄ ⊕i ₁

P ₃₅₁₀ =P ₃₅₁₀ ⊕i ₁

P ₅₀₆₉ =P ₅₀₆₉ ⊕i ₁

P ₆₈₅₉ =P ₆₈₅₉ ⊕i ₁

P ₇₂₄₀ =P ₇₂₄₀ ⊕i ₁

P ₁₁₆₂₄ =P ₁₁₆₂₄ ⊕i ₁

P ₁₂₄₀₈ =P ₁₂₄₀₈ ⊕i ₁

P ₁₂₅₉₀ =P ₁₂₅₉₀ ⊕i ₁

P ₁₂₇₀₀ =P ₁₂₇₀₀ ⊕i ₁

P ₁₃₄₅₀ =P ₁₃₄₅₀ ⊕i ₁

P ₁₃₈₇₂ =P ₁₃₈₇₂ ⊕i ₁

P ₁₄₂₃₁ =P ₁₄₂₃₁ ⊕i ₁

P ₂₁₆₈₄ =P ₂₁₆₈₄ ⊕i ₁

P ₂₄₀₅₄ =P ₂₄₀₅₄ ⊕i ₁

P ₂₄₆₄₁ =P ₂₄₆₄₁ ⊕i ₁

P ₂₅₄₈₄ =P ₂₅₄₈₄ ⊕i ₁

P ₂₅₇₇₅ =P ₂₅₇₇₅ ⊕i ₁

P ₂₆₉₄₄ =P ₂₆₉₄₄ ⊕i ₁

P ₃₁₉₀₇ =P ₃₁₉₀₇ ⊕i ₁

P ₃₄₂₈₁ =P ₃₄₂₈₁ ⊕i ₁

P ₃₅₅₇₀ =P ₃₅₅₇₀ ⊕i ₁

P ₃₆₂₆₁ =P ₃₆₂₆₁ ⊕i ₁

P ₃₆₈₄₈ =P ₃₆₈₄₈ ⊕i ₁

P ₃₇₁₉₃ =P ₃₇₁₉₃ ⊕i ₁

P ₃₇₂₆₀ =P ₃₇₂₆₀ ⊕i ₁

P ₃₇₅₇₆ =P ₃₇₅₇₆ ⊕i ₁

P ₃₇₇₆₆ =P ₃₇₇₆₆ ⊕i ₁  (10)

Herein, i₁ is a 1^(st) information word bit, p_(i) is an ith parity bit, and ⊕ is a binary operation. According to the binary operation, 1⊕1 equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 4) The 360^(th) information word bits i₃₆₀ is accumulated in a parity bit having an address of the parity bit defined in the 2^(nd) row (that is, the row of i=1) of Table 4 as the index of the parity bit.

Step 5) The other 359 information word bits belonging to the same group as that of the information word bit i₃₆₀ are accumulated in the parity bit. In this case, the address of the parity bit may be determined based on Equation 9. However, in this case, x is the address of the parity bit accumulator corresponding to the information word bit i₃₆₀.

Step 6) Steps 4 and 5 described above are repeated for all of the column groups of Table 4.

Step 7) As a result, a parity bit p_(i) is calculated based on Equation 11 presented below. In this case, i is initialized as 1.

p _(i) =p _(i) ⊕p _(i−1) i=1,2, . . . ,N _(ldpc) −K _(ldpc)−1  (11)

In Equation 11, p_(i) is an ith parity bit, N_(ldpc) is a length of an LDPC codeword, K_(ldpc) is a length of an information word of the LDPC codeword, and ⊕ is a binary operation.

As a result, the encoder 110 may calculate the parity bits according to the above-described method.

Referring back to FIG. 1, the encoder 110 may perform the LDPC encoding by using various code rates such as 3/15, 4/15, 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, the encoder 110 may generate an LDPC codeword having various lengths such as 16200, 64800, etc., based on the length of the information word bits and the code rate.

In this case, the encoder 110 may perform the LDPC encoding by using the parity check matrix having the information word submatrix defined by Tables 4 to 8 and the parity submatrix having the dual diagonal configuration (that is, the parity check matrix shown in FIG. 2), or may perform the LDPC encoding by using the parity check matrix which is row and column permutated from the parity check matrix of FIG. 2 based on Equation 4 and Equation 5 (that is, the parity check matrix having the configuration of FIG. 3).

In addition, the encoder 110 may perform Bose, Chaudhuri, Hocquenghem (BCH) encoding as well as the LDPC encoding. To achieve this, the encoder 110 may further include a BCH encoder (not shown) to perform BCH encoding.

In this case, the encoder 110 may perform encoding in an order of BCH encoding and LDPC encoding. Specifically, the encoder 110 may add BCH parity bits to input bits by performing BCH encoding and LDPC-encodes the information word bits including the input bits and the BCH parity bits, thereby generating an LDPC codeword.

The interleaver 120 interleaves the LDPC codeword. That is, the interleaver 120 receives the LDPC codeword from the encoder 110, and interleaves the LDPC codeword based on various interleaving rules.

In particular, the interleaver 120 may interleave the LDPC codeword such that a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword (that is, a plurality of groups or a plurality of blocks) is mapped onto a predetermined bit of a modulation symbol. Accordingly, the modulator 130 may map the bit included in the predetermined group from among the plurality of bit groups constituting the LDPC codeword onto the predetermined bit of the modulation symbol.

Hereinafter, the interleaving rules used in the interleaver 120 will be explained in detail according to cases.

Exemplary Embodiment 1: Case in which a Block Interleaver is Used

According to a first exemplary embodiment, the interleaver 120 may interleave the LDPC codeword in the method as described below, such that the bit included in a predetermined bit group from among the plurality of bit groups constituting the interleaved LDPC codeword is mapped onto a predetermined bit of a modulation symbol. This will be explained below in detail with reference to FIG. 4.

FIG. 4 is a block diagram to illustrate the a configuration of an interleaver according to an exemplary embodiment. Referring to FIG. 4, the interleaver 120 may include a parity interleaver 121, a group interleaver 122 (or a group-wise interleaver 122), a group twist interleaver 123 and a block interleaver 124.

The parity interleaver 121 interleaves the parity bits constituting the LDPC codeword.

Specifically, when the LDPC codeword is generated based on the parity check matrix 200 having the configuration of FIG. 2, the parity interleaver 121 may interleave only the parity bits of the LDPC codeword, among the information word bits and the parity bits of the LDPC codeword, by using Equations 12 presented below:

u _(i) =c _(i) for 0≤i<K _(ldpc), and

u _(K) _(ldpc) _(+M·t+s) =c _(K) _(ldpc) _(+Q) _(ldpc) _(·s+t) for 0≤s<M, 0≤t<Q _(ldpc)  (12),

where M is an interval at which a pattern of a column group is repeated in the information word submatrix 210, that is, the number of columns included in a column group (for example, M=360), and Q_(ldpc) is a size by which each column is cyclic-shifted in the information word submatrix 210. That is, the parity interleaver 121 performs parity interleaving with respect to the LDPC codeword c=(c₀, c₁, . . . , c_(N) _(ldpc) ⁻¹), and outputs U=(u₀, u₁, u_(N) _(ldpc) ⁻¹).

The LDPC codeword which is parity-interleaved in the above-described method may be configured such that a predetermined number of continuous bits of the LDPC codeword have similar decoding characteristics (cycle distribution, a degree of a column, etc.).

For example, the LDPC codeword may have the same characteristics on the basis of M number of continuous bits. Herein, M is an interval at which a pattern of a column group is repeated in the information word submatrix 210 and, for example, may be 360.

Specifically, a product of the LDPC codeword bits and the parity check matrix should be “0”. This means that a sum of products of the i^(th) LDPC codeword bit, c_(i) (i=0, 1, . . . , N_(ldpc)−1) and the i^(th) column of the parity check matrix should be a “0” vector. Accordingly, the i^(th) LDPC codeword bit may be regarded as corresponding to the i^(th) column of the parity check matrix.

In the case of the parity check matrix 200 of FIG. 2, M number of columns in the information word submatrix 210 belong to the same group and the information word submatrix 210 has the same characteristics on the basis of a column group (for example, the columns belonging to the same column group have the same degree distribution and the same cycle characteristic).

In this case, since M number of continuous bits in the information word bits correspond to the same column group of the information word submatrix 210, the information word bits may be formed of M number of continuous bits having the same codeword characteristics. When the parity bits of the LDPC codeword are interleaved by the parity interleaver 121, the parity bits of the LDPC codeword may be formed of M number of continuous bits having the same codeword characteristics.

However, regarding the LDPC codeword encoded based on the parity check matrix 300 of FIG. 3, parity interleaving may not be performed. In this case, the parity interleaver 121 may be omitted.

The group interleaver 122 may divide the parity-interleaved LDPC codeword into a plurality of bit groups and rearrange the order of the plurality of bit groups in bits group wise (group units). That is, the group interleaver 122 may interleave the plurality of bit groups in bits group wise.

To achieve this, the group interleaver 122 divides the parity-interleaved LDPC codeword into a plurality of bit groups by using Equation 13 or Equation 14 presented below.

$\begin{matrix} {\mspace{79mu}{X_{j} = {{\left\{ {{\left. u_{k} \middle| j \right. = \left\lfloor \frac{k}{360} \right\rfloor},{0 \leq k < N_{ldpc}}} \right\}{for}\; 0} \leq j < N_{group}}}} & (13) \\ {X_{j} = {{\left\{ {\left. u_{k} \middle| {{360 \times j} \leq k < {360 \times \left( {j + 1} \right)}} \right.,{0 \leq k < N_{ldpc}}} \right\} for0} \leq j < N_{group}}} & (14) \end{matrix}$

where N_(group) is the total number of bit groups, X_(j) is the i^(th) bit group, and u_(k) is the k^(th) LDPC codeword bit input to the group interleaver 122. In addition,

$\left\lfloor \frac{k}{360} \right\rfloor$

is the largest integer below k/360.

Since 360 in these equations indicates an example of the interval M at which the pattern of a column group is repeated in the information word submatrix, 360 in these equations can be changed to M.

The LDPC codeword which is divided into the plurality of bit groups may be expressed as shown in FIG. 5.

Referring to FIG. 5, the LDPC codeword is divided into the plurality of bit groups and each bit group is formed of M number of continuous bits. When M is 360, each of the plurality of bit groups may be formed of 360 bits. Accordingly, each of the bit groups may be formed of bits corresponding to each of the column groups of the parity check matrix.

Specifically, since the LDPC codeword is divided by M number of continuous bits, K_(ldpc) number of information word bits are divided into (K_(ldpc)/M) number of bit groups, and N_(ldpc)−K_(ldpc) number of parity bits are divided into (N_(ldpc)−K_(ldpc))/M number of bit groups. Accordingly, the LDPC codeword may be divided into (N_(ldpc)/M) number of bit groups in total.

For example, when M=360 and the length N_(ldpc) of the LDPC codeword is 64800, the number of bit groups N_(groups) is 180 (=64800/360), and, when the length N_(ldpc) of the LDPC codeword is 16200, the number of bit groups N_(group) is 45 (16200/360).

As described above, the group interleaver 122 divides the LDPC codeword such that M number of continuous bits are included in a same group since the LDPC codeword has the same codeword characteristics on the basis of M number of continuous bits. Accordingly, when the LDPC codeword is grouped by M number of continuous bits, the bits having the same codeword characteristics belong to the same group.

In the above-described example, the number of bits constituting each bit group is M. However, this is merely an example and the number of bits constituting each bit group is variable.

For example, the number of bits constituting each bit group may be an aliquot part of M. That is, the number of bits constituting each bit group may be an aliquot part of the number of columns constituting a column group of the information word submatrix of the parity check matrix. In this case, each bit group may be formed of an aliquot part of M number of bits. For example, when the number of columns constituting a column group of the information word submatrix is 360, that is, M=360, the group interleaver 122 may divide the LDPC codeword into a plurality of bit groups such that the number of bits constituting each bit group is one of the aliquot parts of 360.

In the following explanation, the number of bits constituting a bit group is M by way of an example, for the convenience of explanation.

Thereafter, the group interleaver 122 interleaves the LDPC codeword in bits group wise. Specifically, the group interleaver 122 may group the LDPC codeword into the plurality of bit groups and rearrange the plurality of bit groups in bits group wise. That is, the group interleaver 122 changes positions of the plurality of bit groups constituting the LDPC codeword and rearranges the order of the plurality of bit groups constituting the LDPC codeword in bits group wise.

According to an exemplary embodiment, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise such that bit groups including bits mapped onto a same modulation symbol from among the plurality of bit groups are spaced apart from one another at a predetermined interval.

In this case, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by considering at least one of the number of rows and columns of the block interleaver 124, the number of bit groups of the LDPC codeword, and the number of bits included in each bit group, such that bit groups including bits mapped onto the same modulation symbol are spaced apart from one another at the predetermined interval.

To achieve this, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by using Equation 15 presented below:

Y _(j) =X _(π(j))(0≤j<N _(group))  (15),

where X_(j) is the j^(th) bit group before group interleaving, and Y_(j) is the j^(th) bit group after group interleaving. In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate, and a modulation method. That is, π(j) denotes a permutation order for group wise interleaving.

Accordingly, X_(π(j)) is a π(j)^(th) bit group before group interleaving, and Equation 15 means that the pre-interleaving π(j)^(th) bit group is interleaved into the j^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 9 to 13 presented below.

In this case, π(j) is defined according to a length of an LPDC codeword and a code rate, and a parity check matrix is also defined according to a length of an LDPC codeword and a code rate. Accordingly, when LDPC encoding is performed based on a specific parity check matrix according to a length of an LDPC codeword and a code rate, the LDPC codeword may be interleaved in bits group wise based on π(j) satisfying the corresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rate of 6/15 to generate an LDPC codeword of a length of 64800, the group interleaver 122 may perform interleaving by using π(j) which is defined according to the length of the LDPC codeword of 64800 and the code rate of 6/15 in Tables 9 to 13 presented below, for example, by using π(j) defined as shown in Table 9.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 1024-Quadrature Amplitude Modulation (QAM), π(j) may be defined as in Table 9 presented below.

TABLE 9 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 66 21 51 55 54 24 33 12 70 63 47 65 block of 56 2 43 64 58 67 53 68 61 39 52 69 Group-wise 25 44 136 29 36 26 126 177 15 37 148 9 interleaver 178 28 34 106 127 76 131 105 138 75 130 101 input, 143 81 32 96 3 78 107 86 98 16 162 150 144 151 90 11 156 100 175 83 155 159 128 88 141 129 146 122 73 112 132 125 174 169 168 79 104 134 82 95 133 164 154 120 110 170 114 153 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 145 8 0 57 23 71 59 14 40 42 62 block of 1 22 31 161 38 30 19 17 18 4 41 Group-wise 13 45 46 152 50 49 27 77 60 35 48 interleaver 167 117 173 113 108 92 135 124 121 97 149 input, 111 158 172 139 74 142 166 7 5 119 20 87 93 103 94 140 165 6 137 157 10 85 84 118 179 147 91 160 163 115 89 80 102 72 109 171 176 99 116 123

In the case of Table 9, Equation 15 may be expressed as Y₀=X_(π(0))=X₆₆, Y₁=X_(π(1))=X₂₁, Y₂=X_(π(2))=X₅₁, . . . , Y₁₇₈=X_(π(178))=X₁₁₆, and Y₁₇₉=X_(π(179))=X₁₂₃. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 66^(th) bit group to the 0^(th) bit group, the 21^(st) bit group to the 1^(st) bit group, the 51^(st) bit group to the 2^(nd) bit group, . . . , the 116^(th) bit group to the 178^(th) bit group, and the 123^(rd) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 10 presented below.

TABLE 10 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 77 48 82 51 57 69 65 6 71 90 84 81 block of 18 38 89 49 93 36 64 47 40 42 76 70 Group-wise 87 67 86 10 1 58 17 14 175 91 68 85 interleaver 83 46 44 102 30 112 122 110 29 20 105 138 input, 28 26 45 24 23 21 157 98 35 95 22 32 159 155 179 160 161 130 123 172 139 124 153 0 148 158 129 163 176 151 171 8 106 144 150 169 142 104 115 135 121 100 12 170 156 126 5 127 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 50 88 61 55 53 73 39 13 79 75 41 block of 56 3 72 2 54 52 145 19 78 80 63 Group-wise 94 15 43 74 60 66 37 92 4 9 16 interleaver 101 174 33 137 136 131 166 59 34 62 125 input, 103 27 113 31 119 173 168 118 120 114 149 109 167 128 107 117 147 177 96 164 152 11 108 162 143 111 141 133 178 134 146 99 132 154 97 140 116 165 7 25

In the case of Table 10, Equation 15 may be expressed as Y₀=X_(π(0))=X₇₇, Y₁=X_(π(1))=X₄₈, Y₂=X_(π(2))=X₈₂, . . . , Y₁₇₈=X_(π(178))=X₇, and Y₁₇₉=X_(π(179))=X₂₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 77^(th) bit group to the 0^(th) bit group, the 48^(th) bit group to the 1^(st) bit group, the 82^(nd) bit group to the 2^(nd) bit group, . . . , the 7^(th) bit group to the 178^(th) bit group, and the 25^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 11 presented below. In particular, when the encoder 110 performs LDPC encoding based on the parity check matrix defined by Table 6, the group interleaver 122 may perform group interleaving by using π(j) defined as in Table 11 presented below:

TABLE 11 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 7 58 108 59 1 14 54 115 57 29 64 65 block of 71 106 50 44 15 52 4 100 90 111 77 89 Group-wise 103 30 105 76 107 88 95 28 66 102 25 39 interleaver 86 45 119 23 79 35 72 33 98 40 38 24 input, 41 97 2 21 61 117 70 62 34 11 67 37 69 139 133 154 160 128 168 84 171 162 31 43 134 126 18 129 137 74 148 147 167 136 164 146 150 16 172 3 155 169 142 156 120 122 19 144 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 8 101 113 60 46 104 87 9 93 81 94 block of 92 5 82 10 116 109 75 91 47 80 99 Group-wise 78 53 118 112 0 83 22 36 51 55 85 interleaver 63 73 20 48 27 96 68 26 110 42 12 input, 49 114 56 32 149 163 173 159 132 170 179 135 123 178 130 127 145 157 176 177 140 151 153 138 161 6 143 124 17 174 131 175 165 158 13 152 141 166 125 121

In the case of Table 11, Equation 15 may be expressed as Y₀=X_(π(0))=X₇, Y₁=X_(π(1))=X₅₈, Y₂=X_(π(2))=X₁₀₈, . . . , Y₁₇₈=X_(π(178))=X₁₂₅, and Y₁₇₉=X_(π(179))=X₁₂₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 7^(th) bit group to the 0^(th) bit group, the 58^(th) bit group to the 1^(st) bit group, the 108^(th) bit group to the 2^(nd) bit group, . . . , the 125^(th) bit group to the 178^(th) bit group, and the 121^(st) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 12 presented below. In particular, when the encoder 110 performs LDPC encoding based on the parity check matrix defined by Table 7, the group interleaver 122 may perform group interleaving by using π(j) defined as in Table 12 presented below:

TABLE 12 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 111 45 78 97 75 63 35 15 9 25 39 94 block of 68 98 31 107 19 110 48 58 71 87 43 62 Group-wise 1 17 61 55 90 56 14 47 77 2 117 20 interleaver 116 29 26 54 38 60 114 59 105 67 103 0 input, 42 51 40 119 8 21 81 76 112 28 34 36 142 141 136 157 162 123 159 150 171 174 137 65 135 52 170 138 127 96 165 156 148 179 163 3 16 144 128 11 175 134 124 130 146 161 145 120 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 24 84 100 49 44 41 32 101 82 23 79 block of 85 70 95 57 10 50 99 118 73 27 12 Group-wise 74 106 83 102 109 113 72 88 115 37 30 interleaver 80 64 4 91 66 46 108 33 104 93 7 input, 86 69 92 53 122 126 131 160 154 6 22 13 177 166 139 167 172 176 153 89 152 168 133 143 121 132 169 147 173 155 149 178 158 129 164 125 5 151 18 140

In the case of Table 12, Equation 15 may be expressed as Y₀=X_(π(0))=X₁₁₁, Y₁=X_(π(1))=X₄₅, Y₂=X_(π(2))=X₇₈, . . . , Y₁₇₈=X_(π(178))=X₁₈, and Y₁₇₉=X_(π(179))=X₁₄₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 111^(th) bit group to the 0^(th) bit group, the 45^(th) bit group to the 1^(st) bit group, the 78^(th) bit group to the 2^(nd) bit group, . . . , the 18^(th) bit group to the 178^(th) bit group, and the 140^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 13 presented below.

TABLE 13 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 91 19 11 106 14 40 20 67 32 22 31 23 block of 133 4 2 21 122 38 12 69 111 81 82 58 Group-wise 80 76 138 87 85 65 130 57 102 83 64 86 interleaver 30 45 94 26 116 98 37 55 44 70 25 7 input, 29 62 50 139 56 109 77 59 127 142 96 105 178 129 18 131 42 165 101 134 36 140 132 103 63 107 162 157 66 104 17 147 167 174 179 3 16 15 148 5 146 163 172 175 151 169 176 150 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 78 68 79 141 117 95 88 136 52 121 1 block of 46 112 60 33 73 53 92 75 48 47 110 Group-wise 100 39 49 125 108 119 6 118 35 61 71 interleaver 34 114 135 128 137 84 51 28 97 27 89 input, 99 90 13 124 120 115 126 143 149 74 41 72 164 93 54 166 43 123 113 0 154 10 173 160 155 161 152 156 177 24 170 9 159 153 171 158 168 144 8 145

In the case of Table 13, Equation 15 may be expressed as Y₀=X_(π(0))=X₉₁, Y₁=X_(π(1))=X₁₉, Y₂=X_(π(2))=X₁₁, . . . , Y₁₇₈=X_(π(178))=X₈, and Y₁₇₉=X_(π(179))=X₁₄₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 91^(st) bit group to the 0^(th) bit group, the 19^(th) bit group to the 1^(st) bit group, the 11^(th) bit group to the 2^(nd) bit group, . . . , the 8^(th) bit group to the 178^(th) bit group, and the 145^(th) bit group to the 179^(th) bit group.

In the above-described examples, the length of the LDPC codeword is 64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, this is merely an example and the interleaving pattern may be defined variously when the length of the LDPC codeword is 16200 or the code rate has different values.

As described above, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by using Equation 15 and Tables 9 to 13.

“j-th block of Group-wise Interleaver output” in Tables 9 to 13 indicates the j-th bit group output from the group interleaver 122 after interleaving, and “π(j)-th block of Group-wise Interleaver input” indicates the π(j)-th bit group input to the group interleaver 122.

In addition, since the order of the bit groups constituting the LDPC codeword is rearranged by the group interleaver 122 in bits group wise, and then the bit groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 9 to 13 in relation to π(j).

π(j) defined as shown in Tables 9 to 13 may be arranged according to the code rates as shown in Table 14 presented below:

TABLE 14 (CR 6/15) (CR 8/15) (CR 10/15) (CR 10/15) (CR 12/15) j-th block of π(j)-th block of π(j)-th block of π(j)-th block of π(j)-th block of π(j)-th block of Group-wise Group-wise Group-wise Group-wise Group-wise Group-wise Interleaver Interleaver Interleaver Interleaver Interleaver Interleaver output input input input input input 0 66 77 7 111 91 1 21 48 58 45 19 2 51 82 108 78 11 3 55 51 59 97 106 4 54 57 1 75 14 5 24 69 14 63 40 6 33 65 54 35 20 7 12 6 115 15 67 8 70 71 57 9 32 9 63 90 29 25 22 10 47 84 64 39 31 11 65 81 65 94 23 12 145 50 8 24 78 13 8 88 101 84 68 14 0 61 113 100 79 15 57 55 60 49 141 16 23 53 46 44 117 17 71 73 104 41 95 18 59 39 87 32 88 19 14 13 9 101 136 20 40 79 93 82 52 21 42 75 81 23 121 22 62 41 94 79 1 23 56 18 71 68 133 24 2 38 106 98 4 25 43 89 50 31 2 26 64 49 44 107 21 27 58 93 15 19 122 28 67 36 52 110 38 29 53 64 4 48 12 30 68 47 100 58 69 31 61 40 90 71 111 32 39 42 111 87 81 33 52 76 77 43 82 34 69 70 89 62 58 35 1 56 92 85 46 36 22 3 5 70 112 37 31 72 82 95 60 38 161 2 10 57 33 39 38 54 116 10 73 40 30 52 109 50 53 41 19 145 75 99 92 42 17 19 91 118 75 43 18 78 47 73 48 44 4 80 80 27 47 45 41 63 99 12 110 46 25 87 103 1 80 47 44 67 30 17 76 48 136 86 105 61 138 49 29 10 76 55 87 50 36 1 107 90 85 51 26 58 88 56 65 52 126 17 95 14 130 53 177 14 28 47 57 54 15 175 66 77 102 55 37 91 102 2 83 56 148 68 25 117 64 57 9 85 39 20 86 58 13 94 78 74 100 59 45 15 53 106 39 60 46 43 118 83 49 61 152 74 112 102 125 62 50 60 0 109 108 63 49 66 83 113 119 64 27 37 22 72 6 65 77 92 36 88 118 66 60 4 51 115 35 67 35 9 55 37 61 68 48 16 85 30 71 69 178 83 86 116 30 70 28 46 45 29 45 71 34 44 119 26 94 72 106 102 23 54 26 73 127 30 79 38 116 74 76 112 35 60 98 75 131 122 72 114 37 76 105 110 33 59 55 77 138 29 98 105 44 78 75 20 40 67 70 79 130 105 38 103 25 80 101 138 24 0 7 81 167 101 63 80 34 82 117 174 73 64 114 83 173 33 20 4 135 84 113 137 48 91 128 85 108 136 27 66 137 86 92 131 96 46 84 87 135 166 68 108 51 88 124 59 26 33 28 89 121 34 110 104 97 90 97 62 42 93 27 91 149 125 12 7 89 92 143 28 41 42 29 93 81 26 97 51 62 94 32 45 2 40 50 95 96 24 21 119 139 96 3 23 61 8 56 97 78 21 117 21 109 98 107 157 70 81 77 99 86 98 62 76 59 100 98 35 34 112 127 101 16 95 11 28 142 102 162 22 67 34 96 103 150 32 37 36 105 104 111 103 49 86 99 105 158 27 114 69 90 106 172 113 56 92 13 107 139 31 32 53 124 108 74 119 149 122 120 109 142 173 163 126 115 110 166 168 173 131 126 111 7 118 159 160 143 112 5 120 132 154 149 113 119 114 170 6 74 114 20 149 179 22 41 115 144 159 69 142 178 116 151 155 139 141 129 117 90 179 133 136 18 118 11 160 154 157 131 119 156 161 160 162 42 120 100 130 128 123 165 121 175 123 168 159 101 122 83 172 84 150 134 123 155 139 171 171 36 124 159 124 162 174 140 125 128 153 31 137 132 126 88 0 43 65 103 127 87 109 135 13 72 128 93 167 123 177 164 129 103 128 178 166 93 130 94 107 130 139 54 131 140 117 127 167 166 132 165 147 145 172 43 133 6 177 157 176 123 134 137 96 176 153 113 135 157 164 177 89 0 136 10 152 140 152 154 137 85 11 151 168 10 138 141 148 134 135 63 139 129 158 126 52 107 140 146 129 18 170 162 141 122 163 129 138 157 142 73 176 137 127 66 143 112 151 74 96 104 144 132 171 148 165 17 145 125 8 147 156 147 146 174 106 167 148 167 147 169 144 136 179 174 148 168 150 164 163 179 149 79 169 146 3 3 150 84 108 153 133 173 151 118 162 138 143 160 152 179 143 161 121 155 153 147 111 6 132 161 154 91 141 143 169 152 155 160 133 124 147 156 156 163 178 17 173 177 157 115 134 174 155 24 158 89 146 131 149 170 159 80 99 175 178 9 160 102 132 165 158 159 161 104 142 150 16 16 162 134 104 16 144 15 163 82 115 172 128 148 164 95 135 3 11 5 165 133 121 155 175 146 166 164 100 169 134 163 167 154 12 142 124 172 168 120 170 156 130 175 169 110 156 120 146 151 170 170 126 122 161 169 171 114 5 19 145 176 172 153 127 144 120 150 173 72 154 158 129 153 174 109 97 13 164 171 175 171 140 152 125 158 176 176 116 141 5 168 177 99 165 166 151 144 178 116 7 125 18 8 179 123 25 121 140 145

“j-th block of Group-wise Interleaver output” in Table 14 indicates the j-th bit group output from the group interleaver 122 after interleaving, and “π(j)-th block of Group-wise Interleaver input” indicates the π(j)-th bit group input to the group interleaver 122. Referring to Table 14, it can be seen that Table 14 is arrangement of data described in Tables 9 to 13 according to the code rates.

The group interleaver 122 may interleave the LDPC codeword in bits group wise by using Equation 16 presented below:

Y _(π(j)) =X _(j)(0≤j<N _(group))  (16),

where X_(j) is the j^(th) bit group before group interleaving, and Y_(j) is the j^(th) bit group after group interleaving. In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate, and a modulation method.

Accordingly, X_(j) is a j^(th) bit group before group interleaving, and Equation 16 means that the pre-interleaving j^(th) bit group is interleaved into the π(i)^(th) bit group.

According to another exemplary embodiment, an example of π(j) may be defined as in Tables 15 to 19 presented below.

In this case, π(j) is defined according to a length of an LPDC codeword and a code rate, and a parity check matrix is also defined according to a length of an LDPC codeword and a code rate. Accordingly, when LDPC encoding is performed based on a specific parity check matrix according to a length of an LDPC codeword and a code rate, the LDPC codeword may be interleaved in bits group wise based on π(j) satisfying the corresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rate of 6/15 to generate an LDPC codeword of a length of 64800, the group interleaver 122 may perform interleaving by using π(j) which is defined according to the length of the LDPC codeword of 64800 and the code rate of 6/15 in Tables 15 to 19 presented below, for example, by using π(j) defined as shown in Table 15.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 15 presented below.

TABLE 15 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 Intput 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 14 35 24 96 44 112 133 111 13 57 136 118 block of 16 5 46 51 64 70 49 40 37 94 6 71 Group-wise 60 10 68 63 62 2 33 29 4 3 23 15 interleaver 34 8 17 173 142 108 78 74 65 97 149 159 output, 86 128 130 164 95 90 100 177 120 80 160 129 157 178 82 151 113 168 89 141 179 88 145 52 77 107 131 138 109 92 115 12 140 153 56 91 38 102 156 166 132 110 81 148 147 170 175 106 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) 12 13 14 15 16 17 18 19 20 21 22 j-th block of 35 36 37 38 39 40 41 42 43 44 45 Group-wise 58 59 60 61 62 63 64 65 66 67 68 interleaver 81 82 83 84 85 86 87 88 89 90 91 Intput 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 7 58 19 54 101 42 43 41 114 1 36 block of 67 50 55 39 32 20 45 21 25 47 59 Group-wise 27 18 66 31 22 9 26 11 0 28 30 interleaver 93 163 122 150 137 99 127 126 158 117 154 output, 161 76 72 98 85 174 169 104 143 84 171 73 125 139 79 75 144 165 162 87 48 134 103 116 61 172 167 123 119 135 105 124 155 83 146 121 176 53 69 152

In the case of Table 15, Equation 16 may be expressed as X₀=Y_(π(0))=Y₁₄, X₁=Y_(π(1))=Y₃₅, X₂=Y_(π(2))=Y₂₄, . . . , X₁₇₈=Y_(π(178))=Y₆₉, and X₁₇₉=Y_(π(179))=Y₁₅₂. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 14^(th) bit group, the 1^(st) bit group to the 35^(th) bit group, the 2^(nd) bit group to the 24^(th) bit group, . . . , the 178^(th) bit group to the 69^(th) bit group, and the 179^(th) bit group to the 152^(nd) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 16 presented below.

TABLE 16 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 intput 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 126 50 38 36 66 171 7 178 145 67 49 137 block of 96 95 179 93 105 92 77 73 107 103 83 89 Group-wise 70 30 1 26 12 3 40 16 39 15 35 4 interleaver 5 34 8 37 17 61 21 33 0 43 20 44 output, 65 27 58 101 134 174 99 159 166 81 72 104 163 176 131 111 108 112 165 75 121 124 91 170 80 123 175 154 161 152 147 41 158 132 138 114 119 151 141 135 177 87 128 110 149 168 144 122 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 intput 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 167 19 53 59 68 52 23 42 78 97 102 block of 100 28 64 24 18 31 22 32 60 71 94 Group-wise 51 88 62 14 90 45 29 6 63 47 56 interleaver 11 2 69 10 57 48 46 13 25 9 55 output, 162 79 146 130 150 127 76 153 74 106 113 172 129 140 120 86 160 155 157 164 85 84 148 143 136 125 173 116 169 98 139 115 118 109 82 54 142 133 156 117

In the case of Table 16, Equation 16 may be expressed as X₀=Y_(π(0))=Y₁₂₆, X₁=Y_(π(1))=Y₅₀, X₂=Y_(π(2))=Y₃₈, . . . , X₁₇₈=Y_(π(178))=Y₁₅₆, and X₁₇₉=Y_(π(179))=Y₁₁₇. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 126^(th) bit group, the 1^(st) bit group to the 50^(th) bit group, the 2^(nd) bit group to the 38^(th) bit group, . . . , the 178^(th) bit group to the 156^(th) bit group, and the 179^(th) bit group to the 117^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 17 presented below. In particular, when the encoder 110 performs LDPC encoding based on the parity check matrix defined by Table 6, the group interleaver 122 may perform group interleaving by using π(j) defined as in Table 17 presented below:

TABLE 17 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 62 4 94 164 29 36 153 0 12 19 38 101 block of 72 80 56 88 85 53 9 47 125 107 76 100 Group-wise 16 43 84 104 25 66 28 59 6 67 106 8 interleaver 115 98 23 75 82 143 41 49 33 58 73 44 output, 35 20 22 52 86 93 77 45 30 13 55 46 7 39 97 60 71 169 179 170 128 155 178 139 151 116 136 176 167 154 172 132 149 145 144 108 152 124 109 148 160 177 146 121 166 113 123 163 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 91 174 5 27 162 156 140 171 83 95 64 block of 74 65 103 79 57 78 92 90 126 26 70 Group-wise 1 3 15 96 99 81 10 11 54 102 87 interleaver 21 37 63 122 68 69 18 51 34 31 42 output, 17 48 24 50 2 40 89 32 61 14 105 131 120 141 130 158 112 117 138 127 147 142 161 137 175 150 118 165 168 133 173 111 119 110 157 159 134 135 129 114

In the case of Table 17, Equation 16 may be expressed as X₀=Y_(π(0))=Y₆₂, X₁=Y_(π(1))=Y₄, X₂=Y_(π(2))=Y₉₄, . . . , X₁₇₈=Y_(π(178))=Y₁₂₉, and X₁₇₉=Y_(π(179))=Y₁₁₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 62^(nd) bit group, the 1^(st) bit group to the 4^(th) bit group, the 2^(nd) bit group to the 94^(th) bit group, . . . , the 178^(th) bit group to the 129^(th) bit group, and the 179^(th) bit group to the 114^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 18 presented below. In particular, when the encoder 110 performs LDPC encoding based on the parity check matrix defined by Table 7, the group interleaver 122 may perform group interleaving by using π(j) defined as in Table 18 presented below:

TABLE 18 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 80 46 55 149 83 176 113 91 96 8 39 164 block of 21 12 9 71 44 101 70 68 25 18 88 102 Group-wise 86 53 29 15 40 93 139 107 72 49 51 38 interleaver 105 36 31 64 43 58 4 99 54 2 22 81 output, 106 90 11 37 143 3 24 41 14 19 61 79 66 69 56 42 95 172 152 108 120 167 175 109 141 130 179 116 115 151 162 171 169 155 146 158 170 119 148 174 144 129 131 137 154 140 123 132 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 45 127 52 7 161 47 178 27 57 97 114 block of 6 103 67 73 10 94 17 92 33 16 1 Group-wise 30 76 74 48 34 5 82 126 85 78 23 interleaver 98 20 60 13 35 104 32 65 135 50 84 output, 89 77 59 26 87 62 28 0 100 63 75 142 163 173 168 110 153 150 166 138 117 125 122 177 136 134 112 157 145 118 160 121 111 156 124 165 133 128 159 147

In the case of Table 18, Equation 16 may be expressed as X₀=Y_(π(0))=Y₈₀, X₁=Y_(π(1))=Y₄₆, X₂=Y_(π(2))=Y₅₅, . . . , X₁₇₈=Y_(π(178))=Y₁₅₉, and X₁₇₉=Y_(π(179))=Y₁₄₇. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 80^(th) bit group, the 1^(st) bit group to the 46^(th) bit group, the 2^(nd) bit group to the 55^(th) bit group, . . . , the 178^(th) bit group to the 159^(th) bit group, and the 179^(th) bit group to the 147^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 19 presented below.

TABLE 19 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 135 22 25 149 24 164 64 80 178 159 137 2 block of 11 157 79 72 90 88 92 69 10 8 38 81 Group-wise 35 44 43 60 94 87 20 40 130 76 96 53 interleaver 30 78 68 127 39 113 42 47 98 12 14 46 output, 41 129 71 17 102 89 74 104 58 121 54 126 109 76 16 65 63 108 21 27 133 107 61 110 48 95 124 15 101 111 177 179 165 145 163 112 153 140 166 128 120 131 146 176 170 158 174 167 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 29 106 4 162 161 144 117 1 6 26 9 block of 66 123 75 28 59 5 114 119 132 77 70 Group-wise 34 99 37 67 93 138 56 51 142 7 13 interleaver 32 33 55 86 50 57 49 18 91 105 0 output, 143 103 3 139 62 97 45 31 36 134 82 100 84 116 52 118 125 23 122 83 19 85 172 169 154 173 136 152 155 141 175 160 151 150 147 168 171 156 115 148

In the case of Table 19, Equation 16 may be expressed as X₀=Y_(π(0))=Y₁₃₅, X₁=Y_(π(1))=Y₂₂, X₂=Y_(π(2))=Y₂₅, . . . , X₁₇₈=Y_(π(178))=Y₁₁₅, and X₁₇₉=Y_(π(179))=Y₁₄₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 135^(th) bit group, the 1^(st) bit group to the 22^(nd) bit group, the 2^(nd) bit group to the 25^(th) bit group, . . . , the 178^(th) bit group to the 115^(th) bit group, and the 179^(th) bit group to the 148^(th) bit group.

In the above-described examples, the length of the LDPC codeword is 64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, this is merely an example and the interleaving pattern may be defined variously when the length of the LDPC codeword is 16200 or the code rate has different values.

As described above, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by using Equation 16 and Tables 15 to 19.

“j-th block of Group-wise Interleaver input” in Tables 15 to 19 indicates the j-th bit group input to the group interleaver 122 before interleaving, and “π(j)-th block of Group-wise Interleaver output” indicates the π(j)-th bit group output from the group interleaver 122 after interleaving.

In addition, since the order of the bit groups constituting the LDPC codeword is rearranged by the group interleaver 122 in bits group wise, and then the bit groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 15 to 19 in relation to π(j).

π(j) defined as shown in Tables 15 to 19 may be arranged according to the code rates as shown in Table 20:

TABLE 20 (CR 6/15) (CR 8/15) (CR 10/15) (CR 10/15) (CR 12/15) j-th block of

 (j)-th block of

 (j)-th block of

 (j)-th block of

 (j)-th block of

 (j)-th block of Group-wise Group-wise Group-wise Group-wise Group-wise Group-wise Interleaver Interleaver Interleaver Interleaver Interleaver Interleaver input output output output output output 0 14 126 62 80 135 1 35 50 4 46 22 2 24 38 94 55 25 3 96 36 164 149 149 4 44 66 29 83 24 5 112 171 36 176 164 6 133 7 153 113 64 7 111 178 0 91 80 8 13 145 12 96 178 9 57 67 19 8 159 10 136 49 38 39 137 11 118 137 101 164 2 12 7 167 91 45 29 13 58 19 174 127 106 14 19 53 5 52 4 15 54 59 27 7 162 16 101 68 162 161 161 17 42 52 156 47 144 18 43 23 140 178 117 19 41 42 171 27 1 20 114 78 83 57 6 21 1 97 95 97 26 22 36 102 64 114 9 23 16 96 72 21 11 24 5 95 80 12 157 25 46 179 56 9 79 26 51 93 88 71 72 27 64 105 85 44 90 28 70 92 53 101 88 29 49 77 9 70 92 30 40 73 47 68 69 31 37 107 125 25 10 32 94 103 107 18 8 33 6 83 76 88 38 34 71 89 100 102 81 35 67 100 74 6 66 36 50 28 65 103 123 37 55 64 103 67 75 38 39 24 79 73 28 39 32 18 57 10 59 40 20 31 78 94 5 41 45 22 92 17 114 42 21 32 90 92 119 43 25 60 126 33 132 44 47 71 26 16 77 45 59 94 70 1 70 46 60 70 16 86 35 47 10 30 43 53 44 48 68 1 84 29 43 49 63 26 104 15 60 50 62 12 25 40 94 51 2 3 66 93 87 52 33 40 28 139 20 53 29 16 59 107 40 54 4 39 6 72 130 55 3 15 67 49 76 56 23 35 106 51 96 57 15 4 8 38 53 58 27 51 1 30 34 59 18 88 3 76 99 60 66 62 15 74 37 61 31 14 96 48 67 62 22 90 99 34 93 63 9 45 81 5 138 64 26 29 10 82 56 65 11 6 11 126 51 66 0 63 54 85 142 67 28 47 102 78 7 68 30 56 87 23 13 69 34 5 115 105 30 70 8 34 98 36 78 71 17 8 23 31 68 72 173 37 75 64 127 73 142 17 82 43 39 74 108 61 143 58 113 75 78 21 41 4 42 76 74 33 49 99 47 77 65 0 33 54 98 78 97 43 58 2 12 79 149 20 73 22 14 80 159 44 44 81 46 81 93 11 21 98 32 82 163 2 37 20 33 83 122 69 63 60 55 84 150 10 122 13 86 85 137 57 68 35 50 86 99 48 69 104 57 87 127 46 18 32 49 88 126 13 51 65 18 89 158 25 34 135 91 90 117 9 31 50 105 91 154 55 42 84 0 92 86 65 35 106 41 93 128 27 20 90 129 94 130 58 22 11 71 95 164 101 52 37 17 96 95 134 86 143 102 97 90 174 93 3 89 98 100 99 77 24 74 99 177 159 45 41 104 100 120 166 30 14 58 101 80 81 13 19 121 102 160 72 55 61 54 103 129 104 46 79 126 104 161 162 17 89 143 105 76 79 48 77 103 106 72 146 24 59 3 107 98 130 50 26 139 108 85 150 2 87 62 109 174 127 40 62 97 110 169 76 89 28 45 111 104 153 32 0 31 112 143 74 61 100 36 113 84 106 14 63 134 114 171 113 105 75 82 115 157 163 7 66 109 116 178 176 39 69 73 117 82 131 97 56 16 118 151 111 60 42 65 119 113 108 71 95 63 120 168 112 169 172 108 121 89 165 179 152 21 122 141 75 170 108 27 123 179 121 128 120 133 124 88 124 155 167 107 125 145 91 178 175 61 126 52 170 139 109 110 127 73 172 131 142 100 128 125 129 120 163 84 129 139 140 141 173 116 130 79 120 130 168 52 131 75 86 158 110 118 132 144 160 112 153 125 133 165 155 117 150 23 134 162 157 138 166 122 135 87 164 127 138 83 136 48 85 147 117 19 137 134 84 142 125 85 138 77 80 151 141 48 139 107 123 116 130 95 140 131 175 136 179 124 141 138 154 176 116 15 142 109 161 167 115 101 143 92 152 154 151 111 144 115 147 172 162 177 145 12 41 132 171 179 146 140 158 149 169 165 147 153 132 145 155 145 148 56 138 144 146 163 149 91 114 108 158 112 150 103 148 161 122 172 151 116 143 137 177 169 152 61 136 175 136 154 153 172 125 150 134 173 154 167 173 118 112 136 155 123 116 165 157 152 156 119 169 168 145 155 157 135 98 133 118 141 158 105 139 173 160 175 159 124 115 111 121 160 160 155 118 119 111 151 161 38 119 152 170 153 162 102 151 124 119 140 163 156 141 109 148 166 164 166 135 148 174 128 165 132 177 160 144 120 166 110 87 177 129 131 167 81 128 146 131 146 168 148 110 121 137 176 169 147 149 166 154 170 170 170 168 113 140 158 171 175 144 123 123 174 172 106 122 163 132 167 173 83 109 110 156 150 174 146 82 157 124 147 175 121 54 159 165 168 176 176 142 134 133 171 177 53 133 135 128 156 178 69 156 129 159 115 179 152 117 114 147 148

Table 14 is the case in which group interleaving is performed using Equation 15 and π(j) is applied as an index of an input bit group, and Table 20 is the case in which group interleaving is performed using Equation 16 and π(j) is applied as an index of an output bit group. Therefore, Tables 14 and 20 have an inverse relationship with each other.

The LDPC codeword which is group-interleaved in the above-described method is illustrated in FIG. 6. Comparing the LDPC codeword of FIG. 6 and the LDPC codeword of FIG. 5 before group interleaving, it can be seen that the order of the plurality of bit groups constituting the LDPC codeword is rearranged.

That is, as shown in FIGS. 5 and 6, the groups of the LDPC codeword are arranged in order of bit group X₀, bit group X₁, . . . , bit group X_(Ngroup−1) before being group-interleaved, and are arranged in an order of bit group Y₀, bit group Y₁, . . . , bit group Y_(Ngroup−1) after being group-interleaved. In this case, the order of arranging the bit groups by the group interleaving may be determined based on Tables 9 to 20.

The group twist interleaver 123 interleaves bits in a same group. That is, the group twist interleaver 123 may rearrange an order of bits in a same bit group by changing the order of the bits in the same bit group.

In this case, the group twist interleaver 123 may rearrange the order of the bits in the same bit group by cyclic-shifting a predetermined number of bits from among the bits in the same bit group.

For example, as shown in FIG. 7, the group twist interleaver 123 may cyclic-shift bits included in the bit group Y₁ to the right by 1 bit. In this case, the bits located in the 0^(th) position, the 1^(st) position, the 2^(nd) position, . . . , the 358^(th) position, and the 359^(th) position in the bit group Y₁ as shown in FIG. 7 are cyclic-shifted to the right by 1 bit. As a result, the bit located in the 359^(th) position before being cyclic-shifted is located in the front of the bit group Y₁ and the bits located in the 0^(th) position, the 1^(st) position, the 2^(nd) position, . . . , the 358^(th) position before being cyclic-shifted are shifted to the right serially by 1 bit and located.

In addition, the group twist interleaver 123 may rearrange the order of bits in each bit group by cyclic-shifting a different number of bits in each bit group.

For example, the group twist interleaver 123 may cyclic-shift the bits included in the bit group Y₁ to the right by 1 bit, and may cyclic-shift the bits included in the bit group Y₂ to the right by 3 bits.

However, the group twist interleaver 123 may be omitted according to circumstances.

In addition, the group twist interleaver 123 is placed after the group interleaver 122 in the above-described example. However, this is merely an example. That is, the group twist interleaver 123 changes only the order of bits in a certain bit group and does not change the order of the bit groups. Therefore, the group twist interleaver 123 may be placed before the group interleaver 122.

The block interleaver 124 interleaves the plurality of bit groups the order of which has been rearranged. Specifically, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged by the group interleaver 122 in bits group wise (or group units). The block interleaver 124 is formed of a plurality of columns each including a plurality of rows, and may interleave by dividing the plurality of rearranged bit groups based on a modulation order determined according to a modulation method.

In this case, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged by the group interleaver 122 in bits group wise. Specifically, the block interleaver 124 may interleave by dividing the plurality of rearranged bit groups according to a modulation order by using a first part and a second part.

Specifically, the block interleaver 124 interleaves by dividing each of the plurality of columns into a first part and a second part, writing the plurality of bit groups in the plurality of columns of the first part serially in bits group wise, dividing bits of the other bit groups into groups (or sub bit groups) each including a predetermined number of bits based on the number of columns, and writing the sub bit groups in the plurality of columns of the second part serially.

Here, the number of bit groups which are interleaved in bits group wise may be determined by at least one of the number of rows and columns constituting the block interleaver 124, the number of bit groups, and the number of bits included in each bit group. In other words, the block interleaver 124 may determine bit groups which are to be interleaved in bits group wise considering at least one of the number of rows and columns constituting the block interleaver 124, the number of bit groups, and the number of bits included in each bit group, interleave the corresponding bit groups in bits group wise, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups. For example, the block interleaver 124 may interleave at least part of the plurality of bit groups in bits group wise using the first part, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups using the second part.

Meanwhile, interleaving bit groups in bits group wise (or in bit group units) means that bits included in a same bit group are written in a same column. In other words, the block interleaver 124, in case of bit groups which are interleaved in bits group wise, may not divide the bits included in the same bit groups and instead write the bits in the same column. However, in case of bit groups which are not interleaved in bits group wise, may divide bits in at least one of these bit groups or each of these bit groups and write the bits in different columns.

Accordingly, the number of rows constituting the first part is an integer multiple of the number of bits included in one bit group (for example, 360), and the number of rows constituting the second part may be less than the number of bits included in this bit group.

In addition, in all bit groups interleaved by the first part, bits included in a same bit group are written and interleaved in a same column of the first part, and in at least one group interleaved by the second part, bits are divided and written in at least two columns of the second part.

The interleaving method will be described later.

Meanwhile, the group twist interleaver 123 changes only an order of bits in a bit group and does not change the order of bit groups by interleaving. Accordingly, an order of bit groups to be block-interleaved by the block interleaver 124, that is, the order of the bit groups to be input to the block interleaver 124, may be determined by the group interleaver 122. For example, the order of the bit groups to be block-interleaved by the block interleaver 124 may be determined by π(j) defined in Tables 9 to 20.

As described above, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged in bits group wise by using the plurality of columns each including the plurality of rows.

In this case, the block interleaver 124 may interleave the LDPC codeword by dividing the plurality of columns into at least two parts. For example, the block interleaver 124 may divide each of the plurality of columns into the first part and the second part and interleave the plurality of bit groups constituting the LDPC codeword.

In this case, the block interleaver 124 may divide each of the plurality of columns into N number of parts (N is an integer greater than or equal to 2) according to whether the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns constituting the block interleaver 124, and may perform interleaving.

When the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns constituting the block interleaver 124, the block interleaver 124 may interleave the plurality of bit groups constituting the LDPC codeword in bits group wise without dividing each of the plurality of columns into parts.

Specifically, the block interleaver 124 may interleave by writing the plurality of bit groups of the LDPC codeword on each of the columns in bits group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bits group wise in a row direction.

In this case, the block interleaver 124 may interleave by writing bits included in a predetermined number of bit groups, which corresponds to a quotient obtained by dividing the number of bit groups of the LDPC codeword by the number of columns of the block interleaver 124, on each of the plurality of columns serially in a column direction, and reading each row of the plurality of columns in which the bits are written in a row direction.

Hereinafter, the bit group located in the j^(th) position after being interleaved by the group interleaver 122 will be referred to as group Y_(j).

For example, it is assumed that the block interleaver 124 is formed of C number of columns each including R₁ number of rows. In addition, it is assumed that the LDPC codeword is formed of N_(group) number of bit groups and the number of bit groups N_(group) is an integer multiple of C.

In this case, when the quotient obtained by dividing N_(group) number of bit groups constituting the LDPC codeword by C number of columns constituting the block interleaver 124 is A (=N_(group)/C) (A is an integer greater than 0), the block interleaver 124 may interleave by writing A (=N_(group)/C) number of bit groups on each column serially in the column direction and reading bits written on each column in the row direction.

For example, as shown in FIG. 8, the block interleaver 124 writes bits included in bit group Y₀, bit group Y₁, . . . , bit group Y_(A−1) in the 1^(st) column from the 1^(st) row to the R₁ ^(th) row, writes bits included in bit group Y_(A), bit group Y_(A+1), . . . , bit group Y_(2A−1) in the 2nd column from the 1^(st) row to the R₁ ^(th) row, . . . , and writes bits included in bit group Y_(CA−A), bit group Y_(CA−A+1), bit group Y_(CA−1) in the column C from the 1^(st) row to the R₁ ^(th) row. The block interleaver 124 may read the bits written in each row of the plurality of columns in the row direction.

Accordingly, the block interleaver 124 interleaves all bit groups constituting the LDPC codeword in bits group wise.

However, when the number of bit groups of the LDPC codeword is not an integer multiple of the number of columns of the block interleaver 124, the block interleaver 124 may divide each column into two parts and interleave a part of the plurality of bit groups of the LDPC codeword in bits group wise, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups. In this case, the bits included in the other bit groups, that is, the bits included in the number of groups which correspond to the remainder when the number of bit groups constituting the LDPC codeword is divided by the number of columns are not interleaved in bits group wise, but interleaved by being divided according to the number of columns.

Specifically, the block interleaver 124 may interleave the LDPC codeword by dividing each of the plurality of columns into two parts.

In this case, the block interleaver 124 may divide the plurality of columns into the first part and the second part based on at least one of the number of rows and columns of the block interleaver 124, the number of bit groups constituting the LDPC codeword, and the number of bits constituting each of the bit groups.

Here, each of the plurality of bit groups may be formed of 360 bits. In addition, the number of bit groups of the LDPC codeword is determined based on the length of the LDPC codeword and the number of bits included in each bit group. For example, when an LDPC codeword in the length of 16200 is divided such that each bit group has 360 bits, the LDPC codeword is divided into 45 bit groups. Alternatively, when an LDPC codeword in the length of 64800 is divided such that each bit group has 360 bits, the LDPC codeword may be divided into 180 bit groups. Further, the number of columns constituting the block interleaver 124 may be determined according to a modulation method. This will be explained in detail below.

Accordingly, the number of rows constituting each of the first part and the second part may be determined based on the number of columns constituting the block interleaver 124, the number of bit groups constituting the LDPC codeword, and the number of bits constituting each of the plurality of bit groups.

Specifically, in each of the plurality of columns, the first part may be formed of as many rows as the number of bits constituting at least one bit group, which can be written in each column in bits group wise, from among the plurality of bit groups of the LDPC codeword, according to the number of columns constituting the block interleaver 124, the number of bit groups constituting the LDPC codeword, and the number of bits constituting each bit group.

In each of the plurality of columns, the second part may be formed of rows excluding as many rows as the number of bits constituting at least some bit groups, which can be written in each of the plurality of columns in bits group wise, from among the plurality of bit groups of the LDPC codeword. Specifically, the number rows of the second part may be the same value as a quotient when the number of bits included in all bit groups excluding bit groups corresponding to the first part is divided by the number of columns constituting the block interleaver 124. In other words, the number of rows of the second part may be the same value as a quotient when the number of bits included in the remaining bit groups which are not written in the first part from among bit groups constituting the LDPC codeword is divided by the number of columns.

That is, the block interleaver 124 may divide each of the plurality of columns into the first part including as many rows as the number of bits included in bit groups which can be written in each column in bits group wise, and the second part including the other rows.

Accordingly, the first part may be formed of as many rows as the number of bits included in bit groups, that is, as many rows as an integer multiple of M. However, since the number of codeword bits constituting each bit group may be an aliquot part of M as described above, the first part may be formed of as many rows as an integer multiple of the number of bits constituting each bit group.

In this case, the block interleaver 124 may interleave by writing and reading the LDPC codeword in the first part and the second part in the same method.

Specifically, the block interleaver 124 may interleave by writing the LDPC codeword in the plurality of columns constituting each of the first part and the second part in a column direction, and reading the plurality of columns constituting the first part and the second part in which the LDPC codeword is written in a row direction.

That is, the block interleaver 124 may interleave by writing the bits included in at least some bit groups, which can be written in each of the plurality of columns in bits group wise among the plurality of bit groups constituting the LDPC codeword, in each of the plurality of columns of the first part serially, dividing the bits included in the other bit groups and writing these divided bits in the plurality of columns of the second part in the column direction, and reading the bits written in each of the plurality of columns constituting each of the first part and the second part in the row direction.

In this case, the block interleaver 124 may interleave by dividing the other bit groups from among the plurality of bit groups constituting the LDPC codeword based on the number of columns constituting the block interleaver 124.

Specifically, the block interleaver 124 may interleave by dividing the bits included in the other bit groups by the number of a plurality of columns, writing each of the divided bits in each of the plurality of columns constituting the second part in the column direction, and reading the plurality of columns constituting the second part, where the divided bits are written, in the row direction.

That is, the block interleaver 124 may divide the bits included in the other bit groups among the plurality of bit groups of the LDPC codeword, that is, the bits in the number of bit groups which correspond to the remainder when the number of bit groups constituting the LDPC codeword is divided by the number of columns, by the number of columns, and may write the divided bits in each column of the second part serially in the column direction.

For example, it is assumed that the block interleaver 124 is formed of C number of columns each including R₁ number of rows. In addition, it is assumed that the LDPC codeword is formed of N_(group) number of bit groups, the number of bit groups N_(group) is not an integer multiple of C, and A×C+1=N_(group) (A is an integer greater than 0). In other words, it is assumed that when the number of bit groups constituting the LDPC codeword is divided by the number of columns, the quotient is A and the remainder is 1.

In this case, as shown in FIGS. 9 and 10, the block interleaver 124 may divide each column into a first part including R₁ number of rows and a second part including R₂ number of rows. In this case, R₁ may correspond to the number of bits included in bit groups which can be written in each column in bits group wise, and R₂ may be R₁ subtracted from the number of rows of each column.

That is, in the above-described example, the number of bit groups which can be written in each column in bits group wise is A, and the first part of each column may be formed of as many rows as the number of bits included in A number of bit groups, that is, may be formed of as many rows as A×M number.

In this case, the block interleaver 124 writes the bits included in the bit groups which can be written in each column in bits group wise, that is, A number of bit groups, in the first part of each column in the column direction.

That is, as shown in FIGS. 9 and 10, the block interleaver 124 writes the bits included in each of bit group Y₀, bit group Y₁, . . . , group Y_(A−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 1^(st) column, writes bits included in each of bit group Y_(A), bit group Y_(A+1), . . . , bit group Y_(2A−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 2^(nd) column, . . . , writes bits included in each of bit group Y_(CA_A), bit group Y_(CA−A+1), . . . , bit group Y_(CA−1) in the 1^(st) to R₁ ^(th) rows of the first part of the column C.

As described above, the block interleaver 124 writes the bits included in the bit groups which can be written in each column in bits group wise in the first part of each column in bits group wise.

In other words, in the above exemplary embodiment, the bits included in each of bit group (Y₀), bit group (Y₁), . . . , bit group (Y_(A−1)) may not be divided and all of the bits may be written in the first column, the bits included in each of bit group (Y_(A)), bit group (Y_(A+1)), . . . , bit group (Y_(2A−1)) may not be divided and all of the bits may be written in the second column, . . . , and the bits included in each of bit group (Y_(CA−A)), bit group (Y_(CA−A+1)), . . . , group (Y_(CA−1)) may not be divided and all of the bits may be written in the C column. As such, bits included in a same bit group in all bit groups interleaved by the first part are written in a same column of the first part.

Thereafter, the block interleaver 124 divides the bits included in the groups other than the bit groups written in the first part of each column from among the plurality of bit groups, and writes these bits in the second part of each column in the column direction. In this case, the block interleaver 124 divides the bits included in the other bit groups such that a same number of bits are written in the second part of each column in the column direction. Here, an order of writing bits in the first part and the second part may be reversed. That is, bits may be written in the second part ahead of the first part according to an exemplary embodiment.

In the above-described example, since A×C+1=N_(group) when the bit groups constituting the LDPC codeword are written in the first part serially, the last bit group Y_(Ngroup−1) of the LDPC codeword is not written in the first part and remains. Accordingly, the block interleaver 124 divides the bits included in the bit group Y_(Ngroup−1) into C number of sub bit groups as shown in FIG. 9, and writes the divided bits (that is, the bits corresponding to the quotient when the bits included in the last group (Y_(Ngroup−1)) are divided by C) in the second part of each column serially.

The bits divided based on the number of columns may be referred to as sub bit groups. In this case, each of the sub bit groups may be written in each column of the second part. That is, the bits included in the bit groups may be divided and may form the sub bit groups.

That is, the block interleaver 124 writes the bits in the 1^(st) to R₂ ^(th) rows of the second part of the 1^(st) column, writes the bits in the 1^(st) to R₂ ^(th) rows of the second part of the 2^(nd) column, . . . , and writes the bits in the 1^(st) to R₂ ^(th) rows of the second part of the column C. In this case, the block interleaver 124 may write the bits in the second part of each column in the column direction as shown in FIG. 9.

That is, in the second part, bits constituting a bit group may not be written in a same column and may be written in a plurality of columns. In other words, in the above example, the last bit group (Y_(Ngroup−1)) is formed of M number of bits and thus, the bits included in the last bit group (Y_(Ngroup−1)) may be divided by M/C and written in each column. That is, the bits included in the last bit group (Y_(Ngroup−1)) are divided by M/C, forming M/C number of sub bit groups, and each of the sub bit groups may be written in each column of the second part.

Accordingly, in at least one bit group which is interleaved by the second part, the bits included in the at least one bit group are divided and written in at least two columns constituting the second part.

In the above-described example, the block interleaver 124 writes the bits in the second part in the column direction. However, this is merely an example. That is, the block interleaver 124 may write the bits in the plurality of columns of the second parts in the row direction. In this case, the block interleaver 124 may write the bits in the first part in the same method as described above.

Specifically, referring to FIG. 10, the block interleaver 124 writes the bits from the 1^(st) row of the second part in the 1^(st) column to the 1^(st) row of the second part in the column C, writes the bits from the 2^(nd) row of the second part in the 1^(st) column to the 2^(nd) row of the second part in the column C, . . . , and writes the bits from the R₂ ^(th) row of the second part in the column to the R₂ ^(th) row of the second part in the column C.

On the other hand, the block interleaver 124 reads the bits written in each row of each part serially in the row direction. That is, as shown in FIGS. 9 and 10, the block interleaver 124 reads the bits written in each row of the first part of the plurality of columns serially in the row direction, and reads the bits written in each row of the second part of the plurality of columns serially in the row direction.

Accordingly, the block interleaver 124 may interleave a part of the plurality of bit groups constituting the LDPC codeword in bits group wise, and divide and interleave some of the remaining bit groups. That is, the block interleaver 124 may interleave by writing the LDPC codeword constituting a predetermined number of bit groups from among the plurality of bit groups in the plurality of columns of the first part in bits group wise, dividing the bits of the other bit groups and writing the bits in each of the columns of the second part, and reading the plurality of columns of the first and second parts in the row direction.

As described above, the block interleaver 124 may interleave the plurality of bit groups in the methods described above with reference to FIGS. 8 to 10.

In particular, in the case of FIG. 9, the bits included in the bit group which does not belong to the first part are written in the second part in the column direction and read in the row direction. In view of this, the order of the bits included in the bit group which does not belong to the first part is rearranged. Since the bits included in the bit group which does not belong to the first part are interleaved as described above, Bit Error Rate (BER)/Frame Error Rate (FER) performance can be improved in comparison with a case in which such bits are not interleaved.

However, the bit group which does not belong to the first part may not be interleaved as shown in FIG. 10. That is, since the block interleaver 124 writes and read the bits included in the bit group which does not belong to the first part in and from the second part in the row direction, the order of the bits included in the bit group which does not belong to the first part is not changed and these bits are output to the modulator 130 serially. In this case, the bits included in the bit group which does not belong to the first part may be output serially to be mapped onto a modulation symbol.

In FIGS. 9 and 10, the last single bit group of the plurality of bit groups is written in the second part. However, this is merely an example. The number of bit groups written in the second part may vary according to the number of bit groups constituting the LDPC codeword, the number of bits constituting each of the bit groups, the number of columns and rows of the block interleaver, the number of transmission antennas, etc.

The block interleaver 124 may have a configuration as shown in Tables 21 and 22 presented below:

TABLE 21 N_(lpdc) = 64800 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 2 4 6 8 10 12 R₁ 32400 16200 10800 7920 6480 5400 R₂ 0 0 0 180 0 0

TABLE 22 N_(ldpc) = 16200 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 2 4 6 8 10 12 R₁ 7920 3960 2520 1800 1440 1080 R₂ 180 90 180 225 180 270

Herein, C (or N_(C)) is the number of columns of the block interleaver 124, R₁ is the number of rows constituting the first part in each column, and R₂ is the number of rows constituting the second part in each column.

Referring to Tables 21 and 22, C is the same value as a modulation order according to a modulation method, and each of a plurality of columns is formed of rows corresponding to a value obtained by dividing the number of bits constituting the LDPC codeword by the number of a plurality of columns.

For example, when the length N_(lpdc) of the LDPC codeword is 64800 and the modulation method is 1024-QAM, the block interleaver 124 is formed of 10 columns as the modulation order is 10 in the case of 1024-QAM, and each column is formed of as many rows as R₁+R₂=6480(=64800/10).

Meanwhile, referring to Tables 21 and 22, when the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves without dividing each column. Therefore, R₁ corresponds to the number of rows constituting each column, and R₂ is 0. In addition, when the number of bit groups constituting the LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 interleaves the groups by dividing each column into the first part formed of R₁ number of rows, and the second part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is equal to the number of bits constituting a modulation symbol as shown in Tables 21 and 22, bits included in a same bit group are mapped onto a single bit of each modulation symbol.

For example, when N_(ldpc)=64800 and the modulation method is 1024-QAM, the block interleaver 124 may be formed of 10 columns each including 6480 rows. In this case, the bits included in each of the plurality of bit groups are written in the 10 columns and bits written in the same row in each column are output serially. In this case, since 10 bits constitute a single modulation symbol in the modulation method of 1024-QAM, bits included in the same bit group, that is, bits output from a single column, may be mapped onto a single bit of each modulation symbol. For example, bits included in a bit group written in the 1^(st) column may be mapped onto a first bit of each modulation symbol.

Referring to Tables 21 and 22, the total number of rows of the block interleaver 124, that is, R₁+R₂, is N_(ldpc)/C.

In addition, the number of rows of the first part, R₁, is an integer multiple of the number of bits included in each group, M (e.g., M=360), and maybe expressed as └N_(group)/C┘×M, and the number of rows of the second part, R₂, may be N_(ldpc)/C−R₁. Herein, └N_(group)/C┘ is the largest integer below N_(group)/C. Since R₁ is an integer multiple of the number of bits included in each group, M, bits may be written in R₁ in bit groups wise.

In addition, when the number of bit groups of the LDPC codeword is not an integer multiple of the number of columns, it can be seen from Tables 21 and 22 that the block interleaver 124 interleaves by dividing each column into two parts.

Specifically, the length of the LDPC codeword divided by the number of columns is the total number of rows included in the each column. In this case, when the number of bit groups of the LDPC codeword is an integer multiple of the number of columns, each column is not divided into two parts. However, when the number of bit groups of the LDPC codeword is not an integer multiple of the number of columns, each column is divided into two parts.

For example, it is assumed that the number of columns of the block interleaver 124 is identical to the number of bits constituting a modulation symbol, and an LDPC codeword is formed of 64800 bits as shown in Table 21. In this case, each bit group of the LDPC codeword is formed of 360 bits, and the LDPC codeword is formed of 64800/360 (=180) bit groups.

When the modulation method is 1024-QAM, the block interleaver 124 may be formed of 10 columns and each column may have 64800/10 (=6480) rows.

In this case, since the number of bit groups of the LDPC codeword divided by the number of columns is 180/10 (=18), bits can be written in each column in bits group wise without dividing each column into two parts. That is, bits included in 18 bit groups which is the quotient when the number of bit groups constituting the LDPC codeword is divided by the number of columns, that is, 18×360 (=6480) bits can be written in each column.

However, when the modulation method is 256-QAM, the block interleaver 124 may be formed of eight (8) columns and each column may have 64800/8 (=8100) rows.

In this case, since the number of bit groups of the LDPC codeword divided by the number of columns is 180/8=22.5, the number of bit groups constituting the LDPC codeword is not an integer multiple of the number of columns. Accordingly, the block interleaver 124 divides each of the eight (8) columns into two parts to perform interleaving in bits group wise.

In this case, since the bits should be written in the first part of each column in bits group wise, the number of bit groups which can be written in the first part of each column in bits group wise is 22 which is the quotient when the number of bit groups constituting the LDPC codeword is divided by the number of columns, and accordingly, the first part of each column has 22×360 (=7920) rows. Accordingly, 7920 bits included in 22 bit groups may be written in the first part of each column.

The second part of each column has rows which are the rows of the first part subtracted from the total rows of each column. Accordingly, the second part of each column includes 8100-7920 (=180) rows.

In this case, bits included in the other bit groups which have not been written in the first part are divided and written in the second part of each column.

Specifically, since 22×8 (=176) bit groups are written in the first part, the number of bit groups to be written in the second part is 180-176 (=4) (for example, a bit group Y₁₇₆, bit group Y₁₇₇, bit group Y₁₇₈, and bit group Y₁₇₉ from among bit group Y₀, bit group Y₁, bit group Y₂, . . . , bit group Y₁₇₈, and bit group Y₁₇₉ constituting the LDPC codeword).

Accordingly, the block interleaver 124 may write the four (4) bit groups which have not been written in the first part and remains from among the bit groups constituting the LDPC codeword in the second part of each column serially.

That is, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y₁₇₆ in the 1^(st) row to the 180^(th) row of the second part of the 1^(st) column in the column direction, and may write the other 180 bits in the 1^(st) row to the 180^(th) row of the second part of the 2^(nd) column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y₁₇₇ in the 1^(st) row to the 180^(th) row of the second part of the 3^(rd) column in the column direction, and may write the other 180 bits in the 1^(st) row to the 180^(th) row of the second part of the 4^(th) column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y₁₇₈ in the 1^(st) row to the 180^(th) row of the second part of the 5^(th) column in the column direction, and may write the other 180 bits in the 1^(st) row to the 180^(th) row of the second part of the 6^(th) column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y₁₇₉ in the 1^(st) row to the 180^(th) row of the second part of the 7^(th) column in the column direction, and may write the other 180 bits in the 1^(st) row to the 180^(th) row of the second part of the 8^(th) column in the column direction.

Accordingly, bits included in a bit group which has not been written in the first part and remains are not written in a same column in the second part and may be divided and written in a plurality of columns.

Hereinafter, the block interleaver 124 of FIG. 4 according to an exemplary embodiment will be explained in detail with reference to FIG. 11.

In a group-interleaved LDPC codeword (v₀, v₁, . . . , v_(N) _(ldpc) ⁻¹), Y_(j) is continuously arranged like V={Y₀, Y₁, . . . , Y_(N) _(ldpc) ⁻¹}.

The LDPC codeword after group interleaving may be interleaved by the block interleaver 124 as shown in FIG. 11. In this case, the block interleaver 124 divides a plurality of columns into the first part (Part 1) and the second part (Part 2) based on the number of columns of the block interleaver 124 and the number of bits of a bit group. In this case, in the first part, bits constituting a bit group may be written in a same column, and in the second part, bits constituting a bit group may be written in a plurality of columns (i.e. bits constituting a bit group may be written in at least two columns).

Specifically, input bits v_(i) are written serially from the first part to the second part column wise, and then read out serially from the first part to the second part row wise. That is, the data bits v_(i) are written serially into the block interleaver column-wise starting in the first part and continuing column-wise finishing in the second part, and then read out serially row-wise from the first part and then row-wise from the second part. Accordingly, each bit included in a same bit group in the first part may be mapped onto a single bit of each modulation symbol.

In this case, the number of columns and the number of rows of the first part and the second part of the block interleaver 124 vary according to a modulation format and a length of the LDPC codeword as in Table 23 presented below. That is, the first part and the second part block interleaving configurations for each modulation format and code length are specified in Table 23 presented below. Herein, the number of columns of the block interleaver 124 may be equal to the number of bits constituting a modulation symbol. In addition, a sum of the number of rows of the first part, N_(r1) and the number of rows of the second part, N_(r2), is equal to N_(ldpc)/N_(C) (herein, N_(C) is the number of columns). In addition, since N_(r1)(=└N_(group)/N_(c)┘×360) is a multiple of 360, a multiple of bits groups may be written in the first part.

TABLE 23 Rows in Part 1 N_(r1) Rows in Part 2 N_(r2) N_(ldpc) = N_(ldpc) = N_(ldpc) = N_(ldpc) = Columns Modulation 64800 16200 64800 16200 N_(c) QPSK 32400 7920 0 180 2  16-QAM 16200 3960 0 90 4  64-QAM 10800 2520 0 180 6  256-QAM 7920 1800 180 225 8 1024-QAM 6480 1440 0 180 10 4096-QAM 5400 1080 0 270 12

Hereinafter, an operation of the block interleaver 124 will be explained in detail.

Specifically, as shown in FIG. 11, the input bit v_(i) (0≤i<N_(C)×N_(r1)) is written in an r_(i) row of a c_(i) column of the first part of the block interleaver 124. Herein, c_(i) and r_(i) are

$c_{i} = \left\lfloor \frac{i}{N_{r1}} \right\rfloor$

and r_(i)=(i mod N_(r1)), respectively.

In addition, the input bit v_(i) (N_(C)×N_(r1)≤i<N_(ldpc)) is written in an r_(i) row of c_(i) column of the second part of the block interleaver 124. Herein, c_(i) and r_(i) satisfy

$c_{i} = \left\lfloor \frac{\left( {i - {N_{C} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor$

and r_(i)=N_(r1)+{(i−N_(C)×N_(r1))mod N_(r2)}, respectively.

An output bit q_(j) (0≤j<N_(ldpc)) is read from a c_(j) column of an r_(j) row. Herein, r_(j) and c_(j) satisfy

$r_{j} = \left\lfloor \frac{j}{N_{c}} \right\rfloor$

and c_(j)=(j mod N_(C)), respectively.

For example, when the length N_(ldpc) of the LDPC codeword is 64800 and the modulation method is 256-QAM, the order of bits output from the block interleaver 124 may be (q₀, q₁, q₂, . . . , q₆₃₃₅₇, q₆₃₃₅₈, q₆₃₃₅₉, q₆₃₃₆₀, q₆₃₃₆₁, . . . , q₆₄₇₉₉)=(v₀, v₇₉₂₀, v₁₅₈₄₀, . . . v₄₇₅₁₉, v₅₅₄₃₉, v₆₃₃₅₉, v₆₃₃₆₀, v₆₃₅₄₀, . . . , v₆₄₇₉₉). Here, the indexes of the right side of the foregoing equation may be specifically expressed for the eight (8) columns as 0, 7920, 15840, 23760, 31680, 39600, 47520, 55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441, . . . , 7919, 15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360, 63540, 63720, 63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719, 63899, 64079, 64259, 64439, 64619, 64799.

Hereinafter, an interleaving operation of the block interleaver 124 will be explained in detail.

The block interleaver 124 may interleave by writing a plurality of bit groups in each column in bits group wise in the column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bits group wise in the row direction.

In this case, the number of columns constituting the block interleaver 124 may vary according to a modulation method, and the number of rows may be the length of the LDPC codeword divided by the number of columns.

For example, when the modulation method is 1024-QAM, the block interleaver 124 may be formed of 10 columns. In this case, when the length N_(ldpc) of the LDPC codeword is 64800, the number of rows is 6480 (=64800/10).

Hereinafter, a method for interleaving the plurality of bit groups in bits group wise by the block interleaver 124 will be explained in detail.

When the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 may interleave by writing the bit groups as many as the number of bit groups divided by the number of columns in each column serially in bits group wise.

For example, when the modulation method is 1024-QAM and the length N_(ldpc) of the LDPC codeword is 64800, the block interleaver 124 may be formed of 10 columns each including 6480 rows. In this case, since the LDPC codeword is divided into (64800/360=180) number of bit groups when the length N_(ldpc) of the LDPC codeword is 64800, the number of bit groups (=180) of the LDPC codeword may be an integer multiple of the number of columns (=10) when the modulation method is 1024-QAM. That is, no remainder is generated when the number of bit groups of the LDPC codeword is divided by the number of columns.

As described above, when the number of bit groups of the LDPC codeword is an integer multiple of the number of columns of the block interleaver 124, the block interleaver 124 may not divide each column into parts and may interleave by writing, in each of the plurality of columns serially in the column direction, the bits included in the bit groups which correspond to the quotient when the number of bits groups of the LDPC codeword is divided by the number of columns of the block interleaver 124, and reading each row of the plurality of columns in which the bits are written in the row direction.

For example, as shown in FIG. 12, the block interleaver 124 writes bits included in each of bit group Y₀, bit group Y₁, . . . , bit group Y₁₇ in the 1^(st) row to 6480^(th) row of the first column, writes bits included in each of bit group Y₁₈, bit group Y₁₉, . . . , bit group Y₃₅ in the 1st row to 6480^(th) row of the second column, . . . , and writes the bits included in each of bit group Y₁₆₂, bit group Y₁₆₃, . . . , bit group Y₁₇₉ in the 1^(st) row to 6480^(th) row of the 10^(th) column. In addition, the block interleaver 124 may read the bits written in each row of the 10 columns serially in the row direction.

As described above, when the number of bit groups constituting an LDPC codeword is an integer multiple of the number of columns of the block interleaver 124, the block interleaver 124 may interleave the plurality of bit groups in bits group wise, and accordingly, bits belonging to a same bit group may be written in a same column.

As described above, the block interleaver 124 may interleave the plurality of bit groups of the LDPC codeword in the methods described above with reference to FIGS. 8 to 12.

When the number of columns constituting the block interleaver 124 has the same value as the modulation degree as in the above-described example, bits included in a same bit group may be mapped onto a single bit of each modulation symbol.

However, this is merely an example and bits included in a same bit group may be mapped onto two bits of each modulation symbol. In this case, the block interleaver 124 may have a configuration as shown in Tables 24 and 25 presented below. In this case, the number of columns constituting the block interleaver 124 may be a half of the modulation order as shown in Tables 24 and 25.

TABLE 24 N_(ldpc) = 64800 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 1 2 3 4 5 6 R₁ 64800 32400 21600 16200 12960 10800 R₂ 0 0 0 0 0 0

TABLE 25 N_(ldpc) = 16200 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 1 2 3 4 5 6 R₁ 16200 7920 5400 3960 3240 2520 R₂ 0 180 0 90 0 180

Herein, C (or N_(C)) is the number of columns of the block interleaver 124, R₁ is the number of rows constituting the first part in each column, and R₂ is the number of rows constituting the second part in each column.

Referring to Tables 24 and 25, when the number of bit groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves without dividing each column. Therefore, R₁ corresponds to the number of rows constituting each column, and R₂ is 0. In addition, when the number of bit groups constituting the LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 interleaves the bit groups by dividing each column into the first part formed of R₁ number of rows, and the second part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is a half of the number of bits constituting the modulation symbol as shown in Tables 24 and 25, bits included in a same bit group may be mapped onto two bits of each modulation symbol.

For example, when N_(ldpc)=64800 and the modulation method is 1024-QAM, the block interleaver 124 may be formed of five (5) columns each including 12960 rows. In this case, a plurality of bit groups constituting an LDPC codeword are written in the five (5) columns in bits group wise and bits written in the same row in respective columns are output serially. In this case, since 10 bits constitute a single modulation symbol in the modulation method of 1024-QAM, bits output from the two rows constitute a single modulation symbol. Accordingly, bits included in a same bit group, that is, bits output from one column, may be mapped onto two bits of a single modulation symbol. For example, bits included in a bit group written in the first column may be mapped onto bits existing in two certain positions of a single modulation symbol.

Referring back to FIG. 1, the modulator 130 maps the interleaved LDPC codeword onto a modulation symbol. Specifically, the modulator 130 may demultiplex the interleaved LDPC codeword, modulate the demultiplexed LDPC codeword, and map the LDPC codeword onto a constellation.

In this case, the modulator 130 may generate a modulation symbol using bits included in each of a plurality of bit groups.

In other words, as described above, bits included in different bit groups may be written in each column of the block interleaver 124, and the block interleaver 124 reads the bits written in each column in the row direction. In this case, the modulator 130 generates a modulation symbol by mapping bits read in each column onto each bit of the modulation symbol. Accordingly, each bit of the modulation symbol may belong to a different group.

For example, it is assumed that a modulation symbol is formed of C number of bits. In this case, bits which are read from each row of C number of columns of the block interleaver 124 may be mapped onto each bit of the modulation symbol and thus, each bit of the modulation symbol formed of C number of bits may belong to C number of different groups.

Hereinbelow, the above feature will be described in greater detail.

First, the modulator 130 may demultiplex the interleaved LDPC codeword. To achieve this, the modulator 130 may include a demultiplexer (not shown) to demultiplex the interleaved LDPC codeword.

A demultiplexer (not shown) demultiplexes the interleaved LDPC codeword. Specifically, the demultiplexer (not shown) performs serial-to-parallel conversion with respect to the interleaved LDPC codeword, and demultiplexes the interleaved LDPC codeword into a cell having a predetermined number of bits (or a data cell).

For example, as shown in FIG. 13, the demultiplexer (not shown) receives an LDPC codeword Q=(q₀, q₁, q₂, . . . ) output from the interleaver 120, outputs the received LDPC codeword bits to a plurality of substreams serially, converts the input LDPC codeword bits into cells, and outputs the cells.

Herein, the number of substreams, N_(substreams), may be equal to the number of bits constituting a modulation symbol, η_(MOD). Accordingly, the number of bits constituting each cell may be equal to the number of bits constituting the modulation symbol (that is, a modulation order).

η_(MOD) may vary according to a modulation method and then number of cells generated may vary according to the length N_(ldpc) of the LDPC codeword as shown in Table 26.

TABLE 26 Number of output Number of output Modulation data cells for data cells for mode μ_(MOD) N_(ldpc) = 64800 N_(ldpc) = 16200 QPSK 2 32400 8100 16-QAM 4 16200 4050 64-QAM 6 10800 2700 256-QAM  8 8100 2025 1024-QAM  10 6480 1620

In this case, bits having a same index in each of the plurality of substreams may constitute a same cell. Accordingly, cells may be configured like (y_(0,0), y_(1,0), . . . , y_(η MOD−1,0))=(q₀, q₁, q_(η MOD−1)), (y_(0,1), y_(1,1), . . . , y_(η MOD−1,1))=(q_(η MOD), q_(η MOD+1), . . . , q_(2×η MOD−1)), . . . .

As described above, the number of substreams, N_(substreams), is equal to the number of bits constituting a modulation symbol, η_(MOD), and the number of bits constituting each cell may be equal to the number of bits constituting the modulation symbol.

The demultiplexer (not shown) may demultiplex input LDPC codeword bits in various methods. That is, the demultiplexer (not shown) may change an order of the LDPC codeword bits and output the bits to each of the plurality of substreams, or may output the bits to each of the plurality of streams serially without changing the order of the LDPC codeword bits. These operations may be determined according to the number of columns used for interleaving in the block interleaver 124.

Specifically, when the block interleaver 124 includes as many columns as half of the number of bits constituting the modulation symbol, the demultiplexer (not shown) may change the order of the input LDPC codeword bits and output the bits to each of the plurality of substreams. An example of a method for changing the order is illustrated in Table 27 presented below:

TABLE 27 Modulation format QPSM input bit 0 1 di mod N_(substreams) output bit-number 0 1 Modulation format 16QAM input bit 0 1 2 3 di mod N_(substreams) output bit-number 0 2 1 3 Modulation format 64 QAM input bit 0 1 2 2 4 5 di mod N_(substreams) output bit-number 0 3 1 4 2 5 Modulation format 256 QAM input bit 0 1 2 3 4 5 6 7 di mod N_(substreams) output bit-number 0 4 1 5 2 6 3 7 Modulation format 1024 QAM input bit 0 1 2 3 4 5 6 7 8 9 di mod N_(substreams) output bit-number 0 5 1 6 2 7 3 5 4 9 Modulation format 4096 QAM input bit 0 1 2 3 4 5 6 7 8 9 10 11 di mod N_(substreams) output bit-number 0 6 1 7 2 6 3 9 4 10 5 11

According to Table 27, when the modulation method is 1024-QAM for example, the number of substreams is 10 since the number of bits constituting a modulation symbol is 10 in the case of 1024-QAM. In this case, the demultiplexer (not shown) may output, from among the serially input bits, bits with an index i satisfying i mod 10=0 to the 0^(th) substream, bits with an index i satisfying i mod 10=1 to the 5^(th) substream, bits with an index i satisfying i mode 10=2 to the 1^(st) substream, bits with an index i satisfying i mode 10=3 to the 6^(th) substream, bits with an index i satisfying i mode 10=4 to the 2^(nd) substream, bits with an index i satisfying i mode 10=5 to the 7^(th) substream, bits with an index i satisfying i mode 10=6 to the 3^(rd) substream, bits with an index i satisfying i mode 10=7 to the 8^(th) substream, bits with an index i satisfying i mode 10=8 to the 4^(th) substream, and bits with an index i satisfying i mode 10=9 to the 9^(th) substream.

Accordingly, the LDPC codeword bits input to the demultiplexer (not shown), (q₀, q₁, q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉, . . . ), may be output as cells like (y_(0,0), y_(1,0), y_(2,0), y_(3,0), y_(4,0), y_(5,0), y_(6,0), y_(7,0), Y_(8,0), y_(9,0))=(q₀, q₅, q₁, q₆, q₂, q₇, q₃, q₈, q₄, q₉), (y_(0,1), y_(1,1), y_(2,1), Y_(3,1), Y_(4,1), y_(5,1), y_(6,1), y_(7,1), y_(8,1), y_(9,1))=(q₁₀, q₁₅, q₁₁, q₁₆, q₁₂, q₁₇, q₁₃, q₁₈, q₁₄, q₁₉), . . . .

When the block interleaver 124 includes the same number of columns as the number of bits constituting a modulation symbol, the demultiplexer (not shown) may output the input LDPC codeword bits to each of the plurality of streams serially without changing the order of the bits. That is, as shown in FIG. 13, the demultiplexer (not shown) may output the input LDPC codeword bits (q₀, q₁, q₂, . . . ) to each of the substreams serially, and accordingly, each cell may be configured as (y_(0,0), y_(1,0), . . . , y_(η MOD−1,0))=(q₀, q₁, . . . , q_(η MOD−1)), (y_(0,1), y_(1,1), . . . , y_(η MOD−1,1))=(q_(η MOD), q_(η MOD+1), . . . , q_(2×η MOD−1)), . . . .

For example, when the modulation method is 1024-QPSK, the number of bits constituting a modulation symbol, η_(MOD), is 10 and thus the number of substreams, N_(substreams), is 10, and cells may be configured like (y_(0,0), y_(1,0), y_(2,0), y_(3,0), y_(4,0), y_(5,0), y_(6,0), y_(7,0), y_(8,0), y_(9,0))=(q₀, q₁, q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉), (y_(0,1), y_(1,1), y_(2,1), y_(3,1), y_(4,1), y_(5,1), y_(6,1), y_(7,1), y_(8,1), y_(9,1))=(q₁₀, q₁₁, q₁₂, q₁₃, q₁₄, q₁₅, q₁₆, q₁₇, q₁₈, q₁₉), (y_(0,2), y_(1,2), y_(2,2), y_(3,2), y_(4,2), y_(5,2), y_(6,2), y_(7,2), y_(8,2), y_(9,2))=(q₂₀, q₂₁, q₂₂, q₂₃, q₂₄, q₂₅, q₂₆, q₂₇, q₂₈, q₂₉)

In the above-described example, the demultiplexer (not shown) may output the input LDPC codeword bits to each of the plurality of substreams serially without changing the order of the LDPC codeword bits. However, this is merely an example. According to an exemplary embodiment, when the block interleaver 124 includes the same number of columns as the number of bits of the modulation symbol, the demultiplexer (not shown) may be omitted.

The modulator 130 may map the demultiplexed LDPC codeword onto modulation symbols. However, when the demultiplexer (not shown) is omitted as described, the modulator 130 may map the LDPC codeword bits output from the interleaver 120, that is, the block-interleaved LDPC codeword bits, onto the modulation symbols.

Specifically, the modulator 130 may modulate the bits (that is, cells) output from the demultiplexer (not shown) in various modulation methods such as QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM. For example, when the modulation method is QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM, the number of bits constituting the modulation symbol, η_(MOD), may be 2, 4, 6, 8, 10 and 12, respectively.

In this case, since each cell output from the demultiplexer (not shown) is formed of as many bits as the number of bits constituting a modulation symbol, the modulator 130 may generate the modulation symbol by mapping each cell output from the demultiplexer (not shown) onto a constellation point serially. Herein, a modulation symbol corresponds to a constellation point on the constellation.

However, the above-described demultiplexer (not shown) may be omitted according to circumstances. In this case, the modulator 130 may generate modulation symbols by grouping a predetermined number of bits from interleaved bits serially and mapping the predetermined number of bits onto constellation points. In this case, the modulator 130 may generate the modulation symbols by mapping η_(MOD) number of bits onto the constellation points serially according to a modulation method.

The modulator 130 may modulate by mapping cells output from the demultiplexer (not shown) onto constellation points in a non-uniform constellation (NUC) method. For example, the modulator 130 may modulate bits output from the demultiplexer (not shown) in various modulation methods such as non-uniform 16-QAM, non-uniform 64-QAM, non-uniform 256-QAM, non-uniform 1024-QAM, non-uniform 4096-QAM, etc.

In the non-uniform constellation method, once a constellation point of the first quadrant is defined, constellation points in the other three quadrants may be determined as follows. For example, when a set of constellation points defined for the first quadrant is X, the set is −conj(X) in the case of the second quadrant, is conj(X) in the case of the third quadrant, and is −(X) in the case of the fourth quadrant.

That is, once the first quadrant is defined, the other quadrants may be expressed as follows:

1 Quarter (first quadrant)=X

2 Quarter (second quadrant)=−conj(X)

3 Quarter (third quadrant)=conj(X)

4 Quarter (fourth quadrant)=−X

Specifically, when the non-uniform M-QAM is used, M number of constellation points may be defined as z={z₀, z₁, . . . , z_(M−1)}. In this case, when the constellation points existing in the first quadrant are defined as {x₀, x₁, x₂, . . . , x_(M/4-1)}, z may be defined as follows:

from z₀ to z_(M/4−1)=from x₀ to x_(M/4)

from z_(M/4) to z_(2×M/4−1)=−conj(from x₀ to x_(M/4))

from z_(2×M/4) to z_(3×M/4−1)=conj(from x₀ to x_(M/4))

from z_(3×M/4) to z_(4×M/4−1)=−(from x₀ to x_(M/4))

Accordingly, the modulator 130 may map the bits [y₀, . . . , y_(m−1)] output from the demultiplexer (not shown) onto constellation points in the non-uniform constellation method by mapping the output bits onto z_(L) having an index of

${L = {\sum\limits_{i = 0}^{m - 1}\left( {y_{1} \times 2^{m - 1}} \right)}}.$

An example of the constellation defined according to the non-uniform 1024-QAM method may be expressed as in Table 28 presented below when the code rate is 6/15, 8/15, 10/15, 12/15. In this case, the constellation point of the first quadrant may be defined with reference to Table 28, and the constellation points in the other three quadrants may be defined in the above-described method.

TABLE 28 Label CR 6/15 CR 8/15 CR 10/15 CR 12/15 (int.) Constellation Constellation Constellation Constellation 0 1.5031 + 1.5031i 1.4800 + 1.4800i 1.4377 + 1.4377i 1.3675 + 1.3675i 1 1.5031 + 1.2286i 1.4800 + 1.2281i 1.4377 + 1.2232i 1.3675 + 1.1917i 2 1.2286 + 1.5031i 1.2281 + 1.4800i 1.2232 + 1.4377i 1.1917 + 1.3675i 3 1.2286 + 1.2286i 1.2281 + 1.2281i 1.2232 + 1.2232i 1.1917 + 1.1917i 4 1.5031 + 0.9418i 1.4800 + 0.9212i 1.4377 + 0.9302i 1.3675 + 0.9386i 5 1.5031 + 1.0048i 1.4800 + 1.0349i 1.4377 + 1.0579i 1.3675 + 1.0529i 6 1.2286 + 0.9418i 1.2281 + 0.9212i 1.2232 + 0.9302i 1.1917 + 0.9386i 7 1.2286 + 1.0048i 1.2281 + 1.0349i 1.2232 + 1.0579i 1.1917 + 1.0529i 8 0.9418 + 1.5031i 0.9212 + 1.4800i 0.9302 + 1.4377i 0.9386 + 1.3675i 9 0.9418 + 1.2286i 0.9212 + 1.2281i 0.9302 + 1.2232i 0.9386 + 1.1917i 10 1.0048 + 1.5031i 1.0349 + 1.4800i 1.0579 + 1.4377i 1.0529 + 1.3675i 11 1.0048 + 1.2286i 1.0349 + 1.2281i 1.0579 + 1.2232i 1.0529 + 1.1917i 12 0.9418 + 0.9418i 0.9212 + 0.9212i 0.9302 + 0.9302i 0.9386 + 0.9386i 13 0.9418 + 1.0048i 0.9212 + 1.0349i 0.9302 + 1.0579i 0.9386 + 1.0529i 14 1.0048 + 0.9418i 1.0349 + 0.9212i 1.0579 + 0.9302i 1.0529 + 0.9386i 15 1.0048 + 1.0048i 1.0349 + 1.0349i 1.0579 + 1.0579i 1.0529 + 1.0529i 16 1.5031 + 0.6097i 1.4800 + 0.5810i 1.4377 + 0.5505i 1.3675 + 0.5763i 17 1.5031 + 0.6072i 1.4800 + 0.5872i 1.4377 + 0.6150i 1.3675 + 0.6531i 18 1.2286 + 0.6097i 1.2281 + 0.5810i 1.2232 + 0.5505i 1.1917 + 0.5763i 19 1.2286 + 0.6072i 1.2281 + 0.5872i 1.2232 + 0.6150i 1.1917 + 0.6531i 20 1.5031 + 0.7196i 1.4800 + 0.7604i 1.4377 + 0.8066i 1.3675 + 0.8324i 21 1.5031 + 0.7113i 1.4800 + 0.7213i 1.4377 + 0.7158i 1.3675 + 0.7417i 22 1.2286 + 0.7196i 1.2281 + 0.7604i 1.2232 + 0.8066i 1.1917 + 0.8324i 23 1.2286 + 0.7113i 1.2281 + 0.7213i 1.2232 + 0.7158i 1.1917 + 0.7417i 24 0.9418 + 0.6097i 0.9212 + 0.5810i 0.9302 + 0.5505i 0.9386 + 0.5763i 25 0.9418 + 0.6072i 0.9212 + 0.5872i 0.9302 + 0.6150i 0.9386 + 0.6531i 26 1.0048 + 0.6097i 1.0349 + 0.5810i 1.0579 + 0.5505i 1.0529 + 0.5763i 27 1.0048 + 0.6072i 1.0349 + 0.5872i 1.0579 + 0.6150i 1.0529 + 0.6531i 28 0.9418 + 0.7196i 0.9212 + 0.7604i 0.9302 + 0.8066i 0.9386 + 0.8324i 29 0.9418 + 0.7113i 0.9212 + 0.7213i 0.9302 + 0.7158i 0.9386 + 0.7417i 30 1.0048 + 0.7196i 1.0349 + 0.7604i 1.0579 + 0.8066i 1.0529 + 0.8324i 31 1.0048 + 0.7113i 1.0349 + 0.7213i 1.0579 + 0.7158i 1.0529 + 0.7417i 32 0.6097 + 1.5031i 0.5810 + 1.4800i 0.5505 + 1.4377i 0.5763 + 1.3675i 33 0.6097 + 1.2286i 0.5810 + 1.2281i 0.5505 + 1.2232i 0.5763 + 1.1917i 34 0.6072 + 1.5031i 0.5872 + 1.4800i 0.6150 + 1.4377i 0.6531 + 1.3675i 35 0.6072 + 1.2286i 0.5872 + 1.2281i 0.6150 + 1.2232i 0.6531 + 1.1917i 36 0.6097 + 0.9418i 0.5810 + 0.9212i 0.5505 + 0.9302i 0.5763 + 0.9386i 37 0.6097 + 1.0048i 0.5810 + 1.0349i 0.5505 + 1.0579i 0.5763 + 1.0529i 38 0.6072 + 0.9418i 0.5872 + 0.9212i 0.6150 + 0.9302i 0.6531 + 0.9386i 39 0.6072 + 1.0048i 0.5872 + 1.0349i 0.6150 + 1.0579i 0.6531 + 1.0529i 40 0.7196 + 1.5031i 0.7604 + 1.4800i 0.8066 + 1.4377i 0.8324 + 1.3675i 41 0.7196 + 1.2286i 0.7604 + 1.2281i 0.8066 + 1.2232i 0.8324 + 1.1917i 42 0.7113 + 1.5031i 0.7213 + 1.4800i 0.7158 + 1.4377i 0.7417 + 1.3675i 43 0.7113 + 1.2286i 0.7213 + 1.2281i 0.7158 + 1.2232i 0.7417 + 1.1917i 44 0.7196 + 0.9418i 0.7604 + 0.9212i 0.8066 + 0.9302i 0.8324 + 0.9386i 45 0.7196 + 1.0048i 0.7604 + 1.0349i 0.8066 + 1.0579i 0.8324 + 1.0529i 46 0.7113 + 0.9418i 0.7213 + 0.9212i 0.7158 + 0.9302i 0.7417 + 0.9386i 47 0.7113 + 1.0048i 0.7213 + 1.0349i 0.7158 + 1.0579i 0.7417 + 1.0529i 48 0.6097 + 0.6097i 0.5810 + 0.5810i 0.5505 + 0.5505i 0.5763 + 0.5763i 49 0.6097 + 0.6072i 0.5810 + 0.5872i 0.5505 + 0.6150i 0.5763 + 0.6531i 50 0.6072 + 0.6097i 0.5872 + 0.5810i 0.6150 + 0.5505i 0.6531 + 0.5763i 51 0.6072 + 0.6072i 0.5872 + 0.5872i 0.6150 + 0.6150i 0.6531 + 0.6531i 52 0.6097 + 0.7196i 0.5810 + 0.7604i 0.5505 + 0.8066i 0.5763 + 0.8324i 53 0.6097 + 0.7113i 0.5810 + 0.7213i 0.5505 + 0.7158i 0.5763 + 0.7417i 54 0.6072 + 0.7196i 0.5872 + 0.7604i 0.6150 + 0.8066i 0.6531 + 0.8324i 55 0.6072 + 0.7113i 0.5872 + 0.7213i 0.6150 + 0.7158i 0.6531 + 0.7417i 56 0.7196 + 0.6097i 0.7604 + 0.5810i 0.8066 + 0.5505i 0.8324 + 0.5763i 57 0.7196 + 0.6072i 0.7604 + 0.5872i 0.8066 + 0.6150i 0.8324 + 0.6531i 58 0.7113 + 0.6097i 0.7213 + 0.5810i 0.7158 + 0.5505i 0.7417 + 0.5763i 59 0.7113 + 0.6072i 0.7213 + 0.5872i 0.7158 + 0.6150i 0.7417 + 0.6531i 60 0.7196 + 0.7196i 0.7604 + 0.7604i 0.8066 + 0.8066i 0.8324 + 0.8324i 61 0.7196 + 0.7113i 0.7604 + 0.7213i 0.8066 + 0.7158i 0.8324 + 0.7417i 62 0.7113 + 0.7196i 0.7213 + 0.7604i 0.7158 + 0.8066i 0.7417 + 0.8324i 63 0.7113 + 0.7113i 0.7213 + 0.7213i 0.7158 + 0.7158i 0.7417 + 0.7417i 64 1.5031 + 0.1275i 1.4800 + 0.0773i 1.4377 + 0.0596i 1.3675 + 0.0354i 65 1.5031 + 0.1276i 1.4800 + 0.0773i 1.4377 + 0.0642i 1.3675 + 0.0921i 66 1.2286 + 0.1275i 1.2281 + 0.0773i 1.2232 + 0.0596i 1.1917 + 0.0354i 67 1.2286 + 0.1276i 1.2281 + 0.0773i 1.2232 + 0.0642i 1.1917 + 0.0921i 68 1.5031 + 0.1295i 1.4800 + 0.1614i 1.4377 + 0.1766i 1.3675 + 0.2185i 69 1.5031 + 0.1294i 1.4800 + 0.1614i 1.4377 + 0.1669i 1.3675 + 0.1602i 70 1.2286 + 0.1295i 1.2281 + 0.1614i 1.2232 + 0.1766i 1.1917 + 0.2185i 71 1.2286 + 0.1294i 1.2281 + 0.1614i 1.2232 + 0.1669i 1.1917 + 0.1602i 72 0.9418 + 0.1275i 0.9212 + 0.0773i 0.9302 + 0.0596i 0.9386 + 0.0354i 73 0.9418 + 0.1276i 0.9212 + 0.0773i 0.9302 + 0.0642i 0.9386 + 0.0921i 74 1.0048 + 0.1275i 1.0349 + 0.0773i 1.0579 + 0.0596i 1.0529 + 0.0354i 75 1.0048 + 0.1276i 1.0349 + 0.0773i 1.0579 + 0.0642i 1.0529 + 0.0921i 76 0.9418 + 0.1295i 0.9212 + 0.1614i 0.9302 + 0.1766i 0.9386 + 0.2185i 77 0.9418 + 0.1294i 0.9212 + 0.1614i 0.9302 + 0.1669i 0.9386 + 0.1602i 78 1.0048 + 0.1295i 1.0349 + 0.1614i 1.0579 + 0.1766i 1.0529 + 0.2185i 79 1.0048 + 0.1294i 1.0349 + 0.1614i 1.0579 + 0.1669i 1.0529 + 0.1602i 80 1.5031 + 0.3666i 1.4800 + 0.4163i 1.4377 + 0.4471i 1.3675 + 0.4947i 81 1.5031 + 0.3675i 1.4800 + 0.4159i 1.4377 + 0.4043i 1.3675 + 0.4264i 82 1.2286 + 0.3666i 1.2281 + 0.4163i 1.2232 + 0.4471i 1.1917 + 0.4947i 83 1.2286 + 0.3675i 1.2281 + 0.4159i 1.2232 + 0.4043i 1.1917 + 0.4264i 84 1.5031 + 0.3424i 1.4800 + 0.3086i 1.4377 + 0.2868i 1.3675 + 0.2910i 85 1.5031 + 0.3431i 1.4800 + 0.3085i 1.4377 + 0.3091i 1.3675 + 0.3530i 86 1.2286 + 0.3424i 1.2281 + 0.3086i 1.2232 + 0.2868i 1.1917 + 0.2910i 87 1.2286 + 0.3431i 1.2281 + 0.3085i 1.2232 + 0.3091i 1.1917 + 0.3530i 88 0.9418 + 0.3666i 0.9212 + 0.4163i 0.9302 + 0.4471i 0.9386 + 0.4947i 89 0.9418 + 0.3675i 0.9212 + 0.4159i 0.9302 + 0.4043i 0.9386 + 0.4264i 90 1.0048 + 0.3666i 1.0349 + 0.4163i 1.0579 + 0.4471i 1.0529 + 0.4947i 91 1.0048 + 0.3675i 1.0349 + 0.4159i 1.0579 + 0.4043i 1.0529 + 0.4264i 92 0.9418 + 0.3424i 0.9212 + 0.3086i 0.9302 + 0.2868i 0.9386 + 0.2910i 93 0.9418 + 0.3431i 0.9212 + 0.3085i 0.9302 + 0.3091i 0.9386 + 0.3530i 94 1.0048 + 0.3424i 1.0349 + 0.3086i 1.0579 + 0.2868i 1.0529 + 0.2910i 95 1.0048 + 0.3431i 1.0349 + 0.3085i 1.0579 + 0.3091i 1.0529 + 0.3530i 96 0.6097 + 0.1275i 0.5810 + 0.0773i 0.5505 + 0.0596i 0.5763 + 0.0354i 97 0.6097 + 0.1276i 0.5810 + 0.0773i 0.5505 + 0.0642i 0.5763 + 0.0921i 98 0.6072 + 0.1275i 0.5872 + 0.0773i 0.6150 + 0.0596i 0.6531 + 0.0354i 99 0.6072 + 0.1276i 0.5872 + 0.0773i 0.6150 + 0.0642i 0.6531 + 0.0921i 100 0.6097 + 0.1295i 0.5810 + 0.1614i 0.5505 + 0.1766i 0.5763 + 0.2185i 101 0.6097 + 0.1294i 0.5810 + 0.1614i 0.5505 + 0.1669i 0.5763 + 0.1602i 102 0.6072 + 0.1295i 0.5872 + 0.1614i 0.6150 + 0.1766i 0.6531 + 0.2185i 103 0.6072 + 0.1294i 0.5872 + 0.1614i 0.6150 + 0.1669i 0.6531 + 0.1602i 104 0.7196 + 0.1275i 0.7604 + 0.0773i 0.8066 + 0.0596i 0.8324 + 0.0354i 105 0.7196 + 0.1276i 0.7604 + 0.0773i 0.8066 + 0.0642i 0.8324 + 0.0921i 106 0.7113 + 0.1275i 0.7213 + 0.0773i 0.7158 + 0.0596i 0.7417 + 0.0354i 107 0.7113 + 0.1276i 0.7213 + 0.0773i 0.7158 + 0.0642i 0.7417 + 0.0921i 108 0.7196 + 0.1295i 0.7604 + 0.1614i 0.8066 + 0.1766i 0.8324 + 0.2185i 109 0.7196 + 0.1294i 0.7604 + 0.1614i 0.8066 + 0.1669i 0.8324 + 0.1602i 110 0.7113 + 0.1295i 0.7213 + 0.1614i 0.7158 + 0.1766i 0.7417 + 0.2185i 111 0.7113 + 0.1294i 0.7213 + 0.1614i 0.7158 + 0.1669i 0.7417 + 0.1602i 112 0.6097 + 0.3666i 0.5810 + 0.4163i 0.5505 + 0.4471i 0.5763 + 0.4947i 113 0.6097 + 0.3675i 0.5810 + 0.4159i 0.5505 + 0.4043i 0.5763 + 0.4264i 114 0.6072 + 0.3666i 0.5872 + 0.4163i 0.6150 + 0.4471i 0.6531 + 0.4947i 115 0.6072 + 0.3675i 0.5872 + 0.4159i 0.6150 + 0.4043i 0.6531 + 0.4264i 116 0.6097 + 0.3424i 0.5810 + 0.3086i 0.5505 + 0.2868i 0.5763 + 0.2910i 117 0.6097 + 0.3431i 0.5810 + 0.3085i 0.5505 + 0.3091i 0.5763 + 0.3530i 118 0.6072 + 0.3424i 0.5872 + 0.3086i 0.6150 + 0.2868i 0.6531 + 0.2910i 119 0.6072 + 0.3431i 0.5872 + 0.3085i 0.6150 + 0.3091i 0.6531 + 0.3530i 120 0.7196 + 0.3666i 0.7604 + 0.4163i 0.8066 + 0.4471i 0.8324 + 0.4947i 121 0.7196 + 0.3675i 0.7604 + 0.4159i 0.8066 + 0.4043i 0.8324 + 0.4264i 122 0.7113 + 0.3666i 0.7213 + 0.4163i 0.7158 + 0.4471i 0.7417 + 0.4947i 123 0.7113 + 0.3675i 0.7213 + 0.4159i 0.7158 + 0.4043i 0.7417 + 0.4264i 124 0.7196 + 0.3424i 0.7604 + 0.3086i 0.8066 + 0.2868i 0.8324 + 0.2910i 125 0.7196 + 0.3431i 0.7604 + 0.3085i 0.8066 + 0.3091i 0.8324 + 0.3530i 126 0.7113 + 0.3424i 0.7213 + 0.3086i 0.7158 + 0.2868i 0.7417 + 0.2910i 127 0.7113 + 0.3431i 0.7213 + 0.3085i 0.7158 + 0.3091i 0.7417 + 0.3530i 128 0.1275 + 1.5031i 0.0773 + 1.4800i 0.0596 + 1.4377i 0.0354 + 1.3675i 129 0.1275 + 1.2286i 0.0773 + 1.2281i 0.0596 + 1.2232i 0.0354 + 1.1917i 130 0.1276 + 1.5031i 0.0773 + 1.4800i 0.0642 + 1.4377i 0.0921 + 1.3675i 131 0.1276 + 1.2286i 0.0773 + 1.2281i 0.0642 + 1.2232i 0.0921 + 1.1917i 132 0.1275 + 0.9418i 0.0773 + 0.9212i 0.0596 + 0.9302i 0.0354 + 0.9386i 133 0.1275 + 1.0048i 0.0773 + 1.0349i 0.0596 + 1.0579i 0.0354 + 1.0529i 134 0.1276 + 0.9418i 0.0773 + 0.9212i 0.0642 + 0.9302i 0.0921 + 0.9386i 135 0.1276 + 1.0048i 0.0773 + 1.0349i 0.0642 + 1.0579i 0.0921 + 1.0529i 136 0.1295 + 1.5031i 0.1614 + 1.4800i 0.1766 + 1.4377i 0.2185 + 1.3675i 137 0.1295 + 1.2286i 0.1614 + 1.2281i 0.1766 + 1.2232i 0.2185 + 1.1917i 138 0.1294 + 1.5031i 0.1614 + 1.4800i 0.1669 + 1.4377i 0.1602 + 1.3675i 139 0.1294 + 1.2286i 0.1614 + 1.2281i 0.1669 + 1.2232i 0.1602 + 1.1917i 140 0.1295 + 0.9418i 0.1614 + 0.9212i 0.1766 + 0.9302i 0.2185 + 0.9386i 141 0.1295 + 1.0048i 0.1614 + 1.0349i 0.1766 + 1.0579i 0.2185 + 1.0529i 142 0.1294 + 0.9418i 0.1614 + 0.9212i 0.1669 + 0.9302i 0.1602 + 0.9386i 143 0.1294 + 1.0048i 0.1614 + 1.0349i 0.1669 + 1.0579i 0.1602 + 1.0529i 144 0.1275 + 0.6097i 0.0773 + 0.5810i 0.0596 + 0.5505i 0.0354 + 0.5763i 145 0.1275 + 0.6072i 0.0773 + 0.5872i 0.0596 + 0.6150i 0.0354 + 0.6531i 146 0.1276 + 0.6097i 0.0773 + 0.5810i 0.0642 + 0.5505i 0.0921 + 0.5763i 147 0.1276 + 0.6072i 0.0773 + 0.5872i 0.0642 + 0.6150i 0.0921 + 0.6531i 148 0.1275 + 0.7196i 0.0773 + 0.7604i 0.0596 + 0.8066i 0.0354 + 0.8324i 149 0.1275 + 0.7113i 0.0773 + 0.7213i 0.0596 + 0.7158i 0.0354 + 0.7417i 150 0.1276 + 0.7196i 0.0773 + 0.7604i 0.0642 + 0.8066i 0.0921 + 0.8324i 151 0.1276 + 0.7113i 0.0773 + 0.7213i 0.0642 + 0.7158i 0.0921 + 0.7417i 152 0.1295 + 0.6097i 0.1614 + 0.5810i 0.1766 + 0.5505i 0.2185 + 0.5763i 153 0.1295 + 0.6072i 0.1614 + 0.5872i 0.1766 + 0.6150i 0.2185 + 0.6531i 154 0.1294 + 0.6097i 0.1614 + 0.5810i 0.1669 + 0.5505i 0.1602 + 0.5763i 155 0.1294 + 0.6072i 0.1614 + 0.5872i 0.1669 + 0.6150i 0.1602 + 0.6531i 156 0.1295 + 0.7196i 0.1614 + 0.7604i 0.1766 + 0.8066i 0.2185 + 0.8324i 157 0.1295 + 0.7113i 0.1614 + 0.7213i 0.1766 + 0.7158i 0.2185 + 0.7417i 158 0.1294 + 0.7196i 0.1614 + 0.7604i 0.1669 + 0.8066i 0.1602 + 0.8324i 159 0.1294 + 0.7113i 0.1614 + 0.7213i 0.1669 + 0.7158i 0.1602 + 0.7417i 160 0.3666 + 1.5031i 0.4163 + 1.4800i 0.4471 + 1.4377i 0.4947 + 1.3675i 161 0.3666 + 1.2286i 0.4163 + 1.2281i 0.4471 + 1.2232i 0.4947 + 1.1917i 162 0.3675 + 1.5031i 0.4159 + 1.4800i 0.4043 + 1.4377i 0.4264 + 1.3675i 163 0.3675 + 1.2286i 0.4159 + 1.2281i 0.4043 + 1.2232i 0.4264 + 1.1917i 164 0.3666 + 0.9418i 0.4163 + 0.9212i 0.4471 + 0.9302i 0.4947 + 0.9386i 165 0.3666 + 1.0048i 0.4163 + 1.0349i 0.4471 + 1.0579i 0.4947 + 1.0529i 166 0.3675 + 0.9418i 0.4159 + 0.9212i 0.4043 + 0.9302i 0.4264 + 0.9386i 167 0.3675 + 1.0048i 0.4159 + 1.0349i 0.4043 + 1.0579i 0.4264 + 1.0529i 168 0.3424 + 1.5031i 0.3086 + 1.4800i 0.2868 + 1.4377i 0.2910 + 1.3675i 169 0.3424 + 1.2286i 0.3086 + 1.2281i 0.2868 + 1.2232i 0.2910 + 1.1917i 170 0.3431 + 1.5031i 0.3085 + 1.4800i 0.3091 + 1.4377i 0.3530 + 1.3675i 171 0.3431 + 1.2286i 0.3085 + 1.2281i 0.3091 + 1.2232i 0.3530 + 1.1917i 172 0.3424 + 0.9418i 0.3086 + 0.9212i 0.2868 + 0.9302i 0.2910 + 0.9386i 173 0.3424 + 1.0048i 0.3086 + 1.0349i 0.2868 + 1.0579i 0.2910 + 1.0529i 174 0.3431 + 0.9418i 0.3085 + 0.9212i 0.3091 + 0.9302i 0.3530 + 0.9386i 175 0.3431 + 1.0048i 0.3085 + 1.0349i 0.3091 + 1.0579i 0.3530 + 1.0529i 176 0.3666 + 0.6097i 0.4163 + 0.5810i 0.4471 + 0.5505i 0.4947 + 0.5763i 177 0.3666 + 0.6072i 0.4163 + 0.5872i 0.4471 + 0.6150i 0.4947 + 0.6531i 178 0.3675 + 0.6097i 0.4159 + 0.5810i 0.4043 + 0.5505i 0.4264 + 0.5763i 179 0.3675 + 0.6072i 0.4159 + 0.5872i 0.4043 + 0.6150i 0.4264 + 0.6531i 180 0.3666 + 0.7196i 0.4163 + 0.7604i 0.4471 + 0.8066i 0.4947 + 0.8324i 181 0.3666 + 0.7113i 0.4163 + 0.7213i 0.4471 + 0.7158i 0.4947 + 0.7417i 182 0.3675 + 0.7196i 0.4159 + 0.7604i 0.4043 + 0.8066i 0.4264 + 0.8324i 183 0.3675 + 0.7113i 0.4159 + 0.7213i 0.4043 + 0.7158i 0.4264 + 0.7417i 184 0.3424 + 0.6097i 0.3086 + 0.5810i 0.2868 + 0.5505i 0.2910 + 0.5763i 185 0.3424 + 0.6072i 0.3086 + 0.5872i 0.2868 + 0.6150i 0.2910 + 0.6531i 186 0.3431 + 0.6097i 0.3085 + 0.5810i 0.3091 + 0.5505i 0.3530 + 0.5763i 187 0.3431 + 0.6072i 0.3085 + 0.5872i 0.3091 + 0.6150i 0.3530 + 0.6531i 188 0.3424 + 0.7196i 0.3086 + 0.7604i 0.2868 + 0.8066i 0.2910 + 0.8324i 189 0.3424 + 0.7113i 0.3086 + 0.7213i 0.2868 + 0.7158i 0.2910 + 0.7417i 190 0.3431 + 0.7196i 0.3085 + 0.7604i 0.3091 + 0.8066i 0.3530 + 0.8324i 191 0.3431 + 0.7113i 0.3085 + 0.7213i 0.3091 + 0.7158i 0.3530 + 0.7417i 192 0.1275 + 0.1275i 0.0773 + 0.0773i 0.0596 + 0.0596i 0.0354 + 0.0354i 193 0.1275 + 0.1276i 0.0773 + 0.0773i 0.0596 + 0.0642i 0.0354 + 0.0921i 194 0.1276 + 0.1275i 0.0773 + 0.0773i 0.0642 + 0.0596i 0.0921 + 0.0354i 195 0.1276 + 0.1276i 0.0773 + 0.0773i 0.0642 + 0.0642i 0.0921 + 0.0921i 196 0.1275 + 0.1295i 0.0773 + 0.1614i 0.0596 + 0.1766i 0.0354 + 0.2185i 197 0.1275 + 0.1294i 0.0773 + 0.1614i 0.0596 + 0.1669i 0.0354 + 0.1602i 198 0.1276 + 0.1295i 0.0773 + 0.1614i 0.0642 + 0.1766i 0.0921 + 0.2185i 199 0.1276 + 0.1294i 0.0773 + 0.1614i 0.0642 + 0.1669i 0.0921 + 0.1602i 200 0.1295 + 0.1275i 0.1614 + 0.0773i 0.1766 + 0.0596i 0.2185 + 0.0354i 201 0.1295 + 0.1276i 0.1614 + 0.0773i 0.1766 + 0.0642i 0.2185 + 0.0921i 202 0.1294 + 0.1275i 0.1614 + 0.0773i 0.1669 + 0.0596i 0.1602 + 0.0354i 203 0.1294 + 0.1276i 0.1614 + 0.0773i 0.1669 + 0.0642i 0.1602 + 0.0921i 204 0.1295 + 0.1295i 0.1614 + 0.1614i 0.1766 + 0.1766i 0.2185 + 0.2185i 205 0.1295 + 0.1294i 0.1614 + 0.1614i 0.1766 + 0.1669i 0.2185 + 0.1602i 206 0.1294 + 0.1295i 0.1614 + 0.1614i 0.1669 + 0.1766i 0.1602 + 0.2185i 207 0.1294 + 0.1294i 0.1614 + 0.1614i 0.1669 + 0.1669i 0.1602 + 0.1602i 208 0.1275 + 0.3666i 0.0773 + 0.4163i 0.0596 + 0.4471i 0.0354 + 0.4947i 209 0.1275 + 0.3675i 0.0773 + 0.4159i 0.0596 + 0.4043i 0.0354 + 0.4264i 210 0.1276 + 0.3666i 0.0773 + 0.4163i 0.0642 + 0.4471i 0.0921 + 0.4947i 211 0.1276 + 0.3675i 0.0773 + 0.4159i 0.0642 + 0.4043i 0.0921 + 0.4264i 212 0.1275 + 0.3424i 0.0773 + 0.3086i 0.0596 + 0.2868i 0.0354 + 0.2910i 213 0.1275 + 0.3431i 0.0773 + 0.3085i 0.0596 + 0.3091i 0.0354 + 0.3530i 214 0.1276 + 0.3424i 0.0773 + 0.3086i 0.0642 + 0.2868i 0.0921 + 0.2910i 215 0.1276 + 0.3431i 0.0773 + 0.3085i 0.0642 + 0.3091i 0.0921 + 0.3530i 216 0.1295 + 0.3666i 0.1614 + 0.4163i 0.1766 + 0.4471i 0.2185 + 0.4947i 217 0.1295 + 0.3675i 0.1614 + 0.4159i 0.1766 + 0.4043i 0.2185 + 0.4264i 218 0.1294 + 0.3666i 0.1614 + 0.4163i 0.1669 + 0.4471i 0.1602 + 0.4947i 219 0.1294 + 0.3675i 0.1614 + 0.4159i 0.1669 + 0.4043i 0.1602 + 0.4264i 220 0.1295 + 0.3424i 0.1614 + 0.3086i 0.1766 + 0.2868i 0.2185 + 0.2910i 221 0.1295 + 0.3431i 0.1614 + 0.3085i 0.1766 + 0.3091i 0.2185 + 0.3530i 222 0.1294 + 0.3424i 0.1614 + 0.3086i 0.1669 + 0.2868i 0.1602 + 0.2910i 223 0.1294 + 0.3431i 0.1614 + 0.3085i 0.1669 + 0.3091i 0.1602 + 0.3530i 224 0.3666 + 0.1275i 0.4163 + 0.0773i 0.4471 + 0.0596i 0.4947 + 0.0354i 225 0.3666 + 0.1276i 0.4163 + 0.0773i 0.4471 + 0.0642i 0.4947 + 0.0921i 226 0.3675 + 0.1275i 0.4159 + 0.0773i 0.4043 + 0.0596i 0.4264 + 0.0354i 227 0.3675 + 0.1276i 0.4159 + 0.0773i 0.4043 + 0.0642i 0.4264 + 0.0921i 228 0.3666 + 0.1295i 0.4163 + 0.1614i 0.4471 + 0.1766i 0.4947 + 0.2185i 229 0.3666 + 0.1294i 0.4163 + 0.1614i 0.4471 + 0.1669i 0.4947 + 0.1602i 230 0.3675 + 0.1295i 0.4159 + 0.1614i 0.4043 + 0.1766i 0.4264 + 0.2185i 231 0.3675 + 0.1294i 0.4159 + 0.1614i 0.4043 + 0.1669i 0.4264 + 0.1602i 232 0.3424 + 0.1275i 0.3086 + 0.0773i 0.2868 + 0.0596i 0.2910 + 0.0354i 233 0.3424 + 0.1276i 0.3086 + 0.0773i 0.2868 + 0.0642i 0.2910 + 0.0921i 234 0.3431 + 0.1275i 0.3085 + 0.0773i 0.3091 + 0.0596i 0.3530 + 0.0354i 235 0.3431 + 0.1276i 0.3085 + 0.0773i 0.3091 + 0.0642i 0.3530 + 0.0921i 236 0.3424 + 0.1295i 0.3086 + 0.1614i 0.2868 + 0.1766i 0.2910 + 0.2185i 237 0.3424 + 0.1294i 0.3086 + 0.1614i 0.2868 + 0.1669i 0.2910 + 0.1602i 238 0.3431 + 0.1295i 0.3085 + 0.1614i 0.3091 + 0.1766i 0.3530 + 0.2185i 239 0.3431 + 0.1294i 0.3085 + 0.1614i 0.3091 + 0.1669i 0.3530 + 0.1602i 240 0.3666 + 0.3666i 0.4163 + 0.4163i 0.4471 + 0.4471i 0.4947 + 0.4947i 241 0.3666 + 0.3675i 0.4163 + 0.4159i 0.4471 + 0.4043i 0.4947 + 0.4264i 242 0.3675 + 0.3666i 0.4159 + 0.4163i 0.4043 + 0.4471i 0.4264 + 0.4947i 243 0.3675 + 0.3675i 0.4159 + 0.4159i 0.4043 + 0.4043i 0.4264 + 0.4264i 244 0.3666 + 0.3424i 0.4163 + 0.3086i 0.4471 + 0.2868i 0.4947 + 0.2910i 245 0.3666 + 0.3431i 0.4163 + 0.3085i 0.4471 + 0.3091i 0.4947 + 0.3530i 246 0.3675 + 0.3424i 0.4159 + 0.3086i 0.4043 + 0.2868i 0.4264 + 0.2910i 247 0.3675 + 0.3431i 0.4159 + 0.3085i 0.4043 + 0.3091i 0.4264 + 0.3530i 248 0.3424 + 0.3666i 0.3086 + 0.4163i 0.2868 + 0.4471i 0.2910 + 0.4947i 249 0.3424 + 0.3675i 0.3086 + 0.4159i 0.2868 + 0.4043i 0.2910 + 0.4264i 250 0.3431 + 0.3666i 0.3085 + 0.4163i 0.3091 + 0.4471i 0.3530 + 0.4947i 251 0.3431 + 0.3675i 0.3085 + 0.4159i 0.3091 + 0.4043i 0.3530 + 0.4264i 252 0.3424 + 0.3424i 0.3086 + 0.3086i 0.2868 + 0.2868i 0.2910 + 0.2910i 253 0.3424 + 0.3431i 0.3086 + 0.3085i 0.2868 + 0.3091i 0.2910 + 0.3530i 254 0.3431 + 0.3424i 0.3085 + 0.3086i 0.3091 + 0.2868i 0.3530 + 0.2910i 255 0.3431 + 0.3431i 0.3085 + 0.3085i 0.3091 + 0.3091i 0.3530 + 0.3530i

Table 28 shows an example of constellation defined according to the non-uniform 1024-QAM. However, this is merely an example. The constellation points may be defined variously in the non-uniform 1024-QAM. In addition, the constellation points may be defined variously in the other modulation methods such as non-uniform 16-QAM, non-uniform 64-QAM, non-uniform 256-QAM, non-uniform 4096-QAM, etc.

The interleaving is performed in the above-described method for the following reasons.

Specifically, when LDPC codeword bits are mapped onto a modulation symbol, the bits may have different reliability (that is, different receiving performance or different probability of reception) according to where the bits are mapped in the modulation symbol. The LDPC codeword bits may have different codeword characteristics according to the configuration of a parity check matrix. That is, the LDPC codeword bits may have different codeword characteristics according to the number of 1 existing in the column of the parity check matrix, that is, the column degree.

Accordingly, the interleaver 120 may interleave to map the LDPC codeword bits having a specific codeword characteristic onto specific bits in the modulation symbol by considering both the codeword characteristics of the LDPC codeword bits and the reliability of the bits constituting the modulation symbol.

For example, it is assumed that the encoder 110 generates an LDPC codeword formed of 64800 bits (N_(ldpc)=64800) by LDPC encoding using a code rate of 6/15, and the modulator 130 uses the non-uniform 1024-QAM modulation method corresponding to the code rate of 6/15 based on Table 28.

In this case, the group interleaver 122 may perform group-interleaving using Equation 15 and Table 9 (or Equation 16 and Table 15). Accordingly, the LDPC codeword formed of bit groups X₀ to X₁₇₉ is interleaved by the group interleaver 122 and the group interleaver 122 may output the bit groups in the order of X₆₆, X₂₁, X₅₁, . . . , X₁₁₆, X₁₂₃.

In this case, the number of columns constituting the block interleaver 124 may be 10 and each column may be formed of 6480 (=360×18) rows. That is, the number of rows of the first part may be 6480 and the number of rows of the second part may be 0.

Accordingly, from among the 180 groups constituting the LDPC codeword, 18 bit groups (X₆₆, X₂₁, X₅₁, X₅₅, X₅₄, X₂₄, X₃₃, X₁₂, X₇₀, X₆₃, X₄₇, X₆₅, X₁₄₅, X₈, X₀, X₅₇, X₂₃, X₇₁) may be inputted to the first part of the 1^(st) column of the block interleaver 124, 18 bit groups (X₅₉, X₁₄, X₄₀, X₄₂, X₆₂, X₅₆, X₂, X₄₃, X₆₄, X₅₈, X₆₇, X₅₃, X₆₈, X₆₁, X₃₉, X₅₂, X₆₉, X₁) may be inputted to the first part of the 2^(nd) column of the block interleaver 124, 18 bit groups (X₂₂, X₃₁, X₁₆₁, X₃₈, X₃₀, X₁₉, X₁₇, X₁₈, X₄, X₄₁, X₂₅, X₄₄, X₁₃₆, X₂₉, X₃₆, X₂₆, X₁₂₆, X₁₇₇) may be inputted to the first part of the 3^(rd) column of the block interleaver 124, 18 bit groups (X₁₅, X₃₇, X₁₄₈, X₉, X₁₃, X₄₅, X₄₆, X₁₅₂, X₅₀, X₄₉, X₂₇, X₇₇, X₆₀, X₃₅, X₄₈, X₁₇₈, X₂₈, X₃₄) may be inputted to the first part of the 4^(th) column of the block interleaver 124, 18 bit groups (X₁₀₆, X₁₂₇, X₇₆, X₁₃₁, X₁₀₅, X₁₃₈, X₇₅, X₁₃₀, X₁₀₁, X₁₆₇, X₁₁₇, X₁₇₃, X₁₁₃, X₁₀₈, X₉₂, X₁₃₅, X₁₂₄, X₁₂₁) may be inputted to the first part of the 5^(th) column of the block interleaver 124, 18 bit groups (X₉₇, X₁₄₉, X₁₄₃, X₈₁, X₃₂, X₉₆, X₃, X₇₈, X₁₀₇, X₈₆, X₉₈, X₁₆, X₁₆₂, X₁₅₀, X₁₁₁, X₁₅₈, X₁₇₂, X₁₃₉) may be inputted to the first part of the 6^(th) column of the block interleaver 124, 18 bit groups (X₇₄, X₁₄₂, X₁₆₆, X₇, X₅, X₁₁₉, X₂₀, X₁₄₄, X₁₅₁, X₉₀, X₁₁, X₁₅₆, X₁₀₀, X₁₇₅, X₈₃, X₁₅₅, X₁₅₉, X₁₂₈) may be inputted to the first part of the 7^(th) column of the block interleaver 124, 18 bit groups (X₈₈, X₈₇, X₉₃, X₁₀₃, X₉₄, X₁₄₀, X₁₆₅, X₆, X₁₃₇, X₁₅₇, X₁₀, X₈₅, X₁₄₁, X₁₂₉, X₁₄₆, X₁₂₂, X₇₃, X₁₁₂) may be inputted to the first part of the 8^(th) column of the block interleaver 124, 18 bit groups (X₁₃₂, X₁₂₅, X₁₇₄, X₁₆₉, X₁₆₈, X₇₉, X₈₄, X₁₁₈, X₁₇₉, X₁₄₇, X₉₁, X₁₆₀, X₁₆₃, X₁₁₅, X₈₉, X₈₀, X₁₀₂, X₁₀₄) may be inputted to the first part of the 9^(th) column of the block interleaver 124, and 18 bit groups (X₁₃₄, X₈₂, X₉₅, X₁₃₃, X₁₆₄, X₁₅₄, X₁₂₀, X₁₁₀, X₁₇₀, X₁₁₄, X₁₅₃, X₇₂, X₁₀₉, X₁₇₁, X₁₇₆, X₉₉, X₁₁₆, X₁₂₃) may be inputted to the first part of the 10^(th) column of the block interleaver 124.

In addition, the block interleaver 124 may output the bits inputted to the 1^(st) row to the last row of each column serially, and the bits outputted from the block interleaver 124 may be inputted to the modulator 130 serially. In this case, the demultiplexer (not shown) may be omitted or the demultiplexer (not shown) may output the inputted bits serially without changing the order of bits.

Accordingly, one bit included in each of the bit groups X₆₆, X₅₉, X₂₂, X₁₅, X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, and X₁₃₄ may constitute one modulation symbol.

As described above, since a specific bit is mapped onto a specific bit in a modulation symbol through interleaving, a receiver side can achieve high receiving performance and high decoding performance.

That is, when LDPC codeword bits of high decoding performance are mapped onto high reliability bits from among bits of each modulation symbol, the receiver side may show high decoding performance, but there is a problem that the LDPC codeword bits of the high decoding performance are not received. In addition, when the LDPC codeword bits of high decoding performance are mapped onto low reliability bits from among the bits of the modulation symbol, initial receiving performance is excellent, and thus, overall performance is also excellent. However, when many bits showing poor decoding performance are received, error propagation may occur.

Accordingly, when LDPC codeword bits are mapped onto modulation symbols, an LDPC codeword bit having a specific codeword characteristic is mapped onto a specific bit of a modulation symbol by considering both codeword characteristics of the LDPC codeword bits and reliability of the bits of the modulation symbol, and is transmitted to the receiver side. Accordingly, the receiver side can achieve both the high receiving performance and the high decoding performance.

The above-described group interleaving and block interleaving is merely an example. In addition to the above-described method, other methods for making one bit included in each of the bit groups X₆₆, X₅₉, X₂₂, X₁₅, X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, and X₁₃₄ constitute one modulation symbol are covered by the inventive concept.

Hereinafter, a method for determining π(j), which is a parameter used for group interleaving, according to various exemplary embodiments, will be explained. First, criteria to be considered are as follows:

Criterion 1) A different interleaving order is used according to a modulation method and a code rate.

Criterion 2) A performance characteristic for each bit group of the LDPC codeword and a performance characteristic for each bit of a modulation symbol should be considered simultaneously.

For example, in the case of the LDPC codeword, the leftmost bits may be good in performance, and the leftmost bits of the modulation symbol may be good in performance. That is, the relative size of receiving performance P(y_(i)) of each of the 10 bits constituting the non-uniform 1024-QAM, y₀, y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, and y₉, has a relationship of P(y₀)=P(y₁)≥P(y₂)=P(y₃)≥P(y₄)=P(y₅)≥P(y₆)=P(y₇)≥P(y₈)=P(y₉).

Therefore, when the length of the LDPC codeword is 64800 and the non-uniform 1024-QAM (or 1024-NUC) is used, onto which bits from among the 10 bits of the non-uniform 1024-QAM the 180 LDPC bit groups are mapped is determined by considering the characteristics of the LDPC codeword and the modulation method simultaneously. In this case, a case having the best estimated performance is determined using a Density evolution method.

That is, a plurality of cases in which 180 bit groups are mapped onto the 10 bits may be considered and a theoretically estimated threshold value may be calculated by applying the density evolution method to each case. When an LDPC code is transmitted as an SNR value, an error probability is 0 in an SNR area greater than the threshold value. Therefore, excellent performance can be guaranteed when the LDPC code is transmitted in the method as in the case of a small threshold value from among the plurality of cases for mapping. However, the method for designing the interleaver 120 based on the density evolution is a theoretical method. Therefore, the interleaver 120 may be designed by verifying the encoding performance based on a really designed parity check matrix and based on a cyclic distribution, in addition to the theoretical method of density evolution.

Meanwhile, when the 180 bits groups are mapped onto the 10 bits, bits groups related to the rows having the same degree in the parity check matrix are grouped into a same group, and, onto which bits from among the 10 1024-QAM bits some of the groups in each group are mapped is determined.

For example, it is assumed that the parity check matrix of the LDPC codeword includes rows having the degrees of 26, 3, and 2, and 14 bit groups, 118 bit groups, and 36 bit groups are related to the rows having the degrees 26, 3, and 2, respectively,

In the case of the non-uniform 1024-QAM method, two bits have the same receiving performance (that is, the same probability of reception) (that is, P(y₀)=P(y₁), P(y₂)=P(y₃), P(y₄)=P(y₅), P(y₆)=P(y₇), P(y₈)=P(y₉)), and thus the bit groups may be mapped onto five (5) bits. Therefore, the number of cases where the bit groups are mapped onto the five (5) bits may be expressed as follows:

Number of cases modulated bits degree where bits are mapped y₀, y₁ 26  ₁₄C_(x1) y₂, y₃ 3 ₁₁₈C_(w1) 2   ₃₆C_(z1) 26  ₁₄C_(x2) 3 ₁₁₈C_(w2) 2 ₃₆C_(/7) y₄, y₅ 26  ₁₄C_(x3) 3 ₁₁₈C_(w3) 2   ₃₆C_(z3) y₆, y₇ 26  ₁₄C_(x4) 3 ₁₁₈C_(w4) 2   ₃₆C_(z4) y₈, y₉ 26  ₁₄C_(x5) 3 ₁₁₈C_(w5) 2   ₃₆C_(z5) sum 180

That is, regarding the bit groups to be mapped onto y₀ and y₁, the number of cases where x₁ number of bit groups are selected from among the bit groups related to the rows having the degree of 26, w₁ number of bit groups are selected from among the bit groups related to the rows having the degree of three (3), and z₁ number of bit groups are selected from among the bit groups related to the rows having the degree of two (2) may be ₁₄C_(x1)+₁₁₈C_(w1)+₃₆C_(z1).

In addition, regarding the bit groups to be mapped onto y₂ and y₃, the number of cases where x₂ number of bit groups are selected from among the bit groups related to the rows having the degree of 26, w₂ number of bit groups are selected from among the bit groups related to the rows having the degree of three (3), and z₂ number of bit groups are selected from among the bit groups related to the rows having the degree of two (2) may be ₁₄C_(x2)+₁₁₈C_(w2)+₃₆C_(z2).

In addition, regarding the bit groups to be mapped onto y₄ and y₅, the number of cases where x₃ number of bit groups are selected from among the bit groups related to the rows having the degree of 26, w₃ number of bit groups are selected from among the bit groups related to the rows having the degree of three (3), and z₃ number of bit groups are selected from among the bit groups related to the rows having the degree of two (2) may be ₁₄C_(x3)+₁₁₈C_(w3)+₃₆C_(z3).

In addition, regarding the bit groups to be mapped onto y₆ and y₇, the number of cases where x₄ number of bit groups are selected from among the bit groups related to the rows having the degree of 26, w₄ number of bit groups are selected from among the bit groups related to the rows having the degree of three (3), and z₄ number of bit groups are selected from among the bit groups related to the rows having the degree of two (2) may be ₁₄C_(x4)+₁₁₈C_(w4)+₃₆C_(z4).

In addition, regarding the bit groups to be mapped onto y₈ and y₉, the number of cases where x₅ number of bit groups are selected from among the bit groups related to the rows having the degree of 26, w₅ number of bit groups are selected from among the bit groups related to the rows having the degree of three (3), and z₅ number of bit groups are selected from among the bit groups related to the rows having the degree of two (2) may be ₁₄C_(x5)+₁₁₈C_(w5)+₃₆C_(z5).

In this case, x₁+x₂+x₃+x₄+x₅=14, w₁+w₂+w₃+w₄+W₅=118, and z₁+z₂+z₃+z₄+z₅=36.

However, since there are a large number of cases in the above example, it may be difficult to estimate performance for each case through density evolution.

Therefore, the number of cases may be calculated by reducing the number of kinds of receiving performance, and then performance for each case may be estimated through density evolution.

For example, on the assumption that the probability of reception of y₀, y₁, y₂, and y₃ is the same and the probability of reception of y₄, y₅, y₆, y₇, y₈, and y₉ is the same as shown in a table presented below, the number of cases where the bit groups are mapped onto three (3) bits may be calculated.

Number of cases modulated bits degree where bits are mapped y₀, y₁, y₂, y₃ 26 ₁₄C_(x1) 3 ₁₁₈C_(w1 ) 2 ₃₆C_(z1) y₄ y₅, y₆, y₇, y₈, y₉ 26 ₁₄C_(x2) 3 ₁₁₈C_(w2 ) 2 ₃₆C_(z2) sum 180

That is, regarding the bit groups to be mapped onto y₀, y₁, y₂, y₃, the number of cases where x₁ number of bit groups are selected from among the bit groups related to the rows having the degree of 26, w₁ number of bit groups are selected from among the bit groups related to the rows having the degree of three (3), and z₁ number of bit groups are selected from among the bit groups related to the rows having the degree of two (2) may be ₁₄C_(x1)+₁₁₈C_(w1)+36C_(z1).

In addition, regarding the bit groups to be mapped onto y₄, y₅, y₆, y₇, y₈, y₉, the number of cases where x₂ number of bit groups are selected from among the bit groups related to the rows having the degree of 26, w₂ number of bit groups are selected from among the bit groups related to the rows having the degree of three (3), and z₂ number of bit groups are selected from among the bit groups related to the rows having the degree of two (2) may be ₁₄C_(x2)+₁₁₈C_(w2)+₃₆C_(z2).

In this case, x₁+x₂=14, w₁+w₂=118, and z₁+z₂=36.

Thereafter, after the performance for each case is estimated through density devolution, the case which is estimated to have the best performance is selected. That is, how many bit groups should be selected from each of the bit groups related to the rows having the degrees of 26, 3, and 2 and mapped onto y₀, y₁, y₂, y₃, and y₄, y₅, y₆, y₇, y₈, y₉ in order to have the best performance is determined through density evolution, and x₁, x₂, w₁, w₁, z¹, z² are determined.

Thereafter, the bits which are assumed to have the same receiving performance are determined to have different receiving performance, and the above-described process is repeated.

That is, the number of cases where the bit groups are mapped onto y₀, y₁, y₂, y₃ within x₁, w₁, z₁ is calculated based on determined x₁, w₁, z₁, and performance for each case is estimated through density evolution and the case which is estimated to have the best performance is selected.

In addition, the number of cases where the bit groups are mapped onto y₄, y₅, y₆, y₇, y₈, y₉ within x₂, w₂, z₂ is calculated based on determined x₂, w₂, z₂, and performance for each case is estimated through density evolution and the case which is estimated to have the best performance is selected.

Accordingly, how many of the bit groups related to the rows having each of the degrees should be mapped onto the 1024-QAM bits to have the best performance may be determined, and the interleaver 120 may be designed to be able to map a specific group of the LDPC codeword onto a specific bit of the modulation symbol and satisfy the case of the best performance.

In the above-described method, the group interleaving method can be designed.

The transmitting apparatus 200 may transmit the signal mapped onto the constellation to a receiving apparatus (for example, 2700 of FIG. 18). For example, the transmitting apparatus 200 may map the signal mapped onto the constellation onto an Orthogonal Frequency Division Multiplexing (OFDM) frame using OFDM, and may transmit the signal to the receiving apparatus 2700 through an allocated channel.

Exemplary Embodiment 2: Case in which a Block-Row Interleaver is Used

According to another exemplary embodiment, the interleaver 120 may interleave an LDPC codeword in other methods, different from the methods described in above Exemplary Embodiment 1, and may map bits included in a predetermined bit group from among a plurality of bit groups constituting the interleaved LDPC codeword onto a predetermined bit of a modulation symbol. This will be explained in detail with reference to FIG. 14.

Referring to FIG. 14, the interleaver 120 includes a parity interleaver 121, a group interleaver (or a group-wise interleaver 122), a group twist interleaver 123 and a block-row interleaver 125. Herein, the parity interleaver 121 and the group twist interleaver 123 perform the same functions as in Exemplary Embodiment 1 described above, and thus, a detailed description of these elements is omitted.

The group interleaver 122 may divide a parity-interleaved LDPC codeword into a plurality of bit groups, and may rearrange the order of the plurality of bit groups in bits group wise.

In this case, the operation of dividing the parity-interleaved LDPC codeword into the plurality of bit groups is the same as in Exemplary Embodiment 1, and thus, a detailed description thereof is omitted.

The group interleaver 122 interleaves the LDPC codeword in bits group wise. Specifically, the group interleaver 122 may group the LDPC codeword into the plurality of bit groups, and may rearrange the plurality of bit groups in bits group wise. That is, the group interleaver 122 may rearrange the order of the plurality of bit groups in the LDPC codeword in group units by changing locations of the plurality of bit groups constituting the LDPC codeword.

Herein, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise such that bit groups including bits mapped onto the same modulation symbol from among the plurality of bit groups are serially arranged.

In this case, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by considering at least one of the number of rows and columns of the block-row interleaver 124, the number of bit groups of the LDPC codeword, and the number of bits included in each bit group, such that bit groups including bits mapped onto the same modulation symbol are serially arranged.

To achieve this, the group interleaver 122 may interleave the LDPC codeword in bits group wise by using Equation 17 presented below:

Y _(j) =x _(π(j))(0≤j<N _(group))  (17),

where X_(j) is the j^(th) bit group before group interleaving, and Y_(j) is the j^(th) bit group after group interleaving. In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate, and a modulation method.

Accordingly, X_(π(j)) is a π(j)^(th) bit group before group interleaving, and Equation 17 means that the pre-interleaving π(j)^(th) bit group is interleaved into the j^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 29 to 33 presented below.

In this case, π(j) is defined according to a length of an LPDC codeword and a code rate, and a parity check matrix is also defined according to a length of an LDPC codeword and a code rate. Accordingly, when LDPC encoding is performed based on a specific parity check matrix according to a length of an LDPC codeword and a code rate, the LDPC codeword may be interleaved in bits group wise based on π(j) satisfying the corresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rate of 6/15 to generate an LDPC codeword of a length of 64800, the group interleaver 122 may perform interleaving by using π(j) which is defined according to the length of the LDPC codeword of 64800 and the code rate of 6/15 in Tables 29 to 33 presented below, for example, by using π(j) defined as shown in Table 29.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 29 presented below.

TABLE 29 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 66 59 22 15 106 97 74 88 132 134 21 14 block of 148 76 143 166 93 174 95 55 42 38 9 131 Group-wise 5 94 168 164 24 56 19 45 138 96 119 140 interleaver 120 12 43 18 152 130 78 144 6 118 110 70 input, 41 49 167 86 90 157 147 114 47 67 25 27 16 156 85 160 72 145 68 136 60 113 162 100 115 171 0 39 36 48 92 111 83 146 89 176 69 126 28 124 172 159 73 102 116 71 1 177 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 31 37 127 149 142 87 125 82 51 40 161 block of 81 7 103 169 133 54 62 30 13 105 32 Group-wise 79 154 33 2 17 46 75 3 20 165 84 interleaver 64 4 50 101 107 151 137 179 170 63 58 input, 117 98 11 10 91 153 65 53 44 77 173 141 163 109 8 61 29 35 108 150 175 129 57 52 26 178 135 158 155 122 80 99 23 34 121 139 128 112 104 123

In the case of Table 29, Equation 17 may be expressed as Y₀=X_(π(0))=X₆₆, Y₁=X_(π(1))=X₅₉, Y₂=X_(π(2))=X₂₂, . . . , Y₁₇₈=X_(π(178))=X₁₀₄, and Y₁₇₉=X_(π(179))=X₁₂₃. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 66^(th) bit group to the 0^(th) bit group, the 59^(th) bit group to the 1^(st) bit group, the 22^(nd) bit group to the 2^(nd) bit group, . . . , the 104^(th) bit group to the 178^(th) bit group, and the 123^(rd) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 30 presented below.

TABLE 30 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 77 39 3 175 102 62 119 0 171 104 48 13 block of 68 112 28 168 167 106 135 51 75 54 85 122 Group-wise 120 107 150 100 69 18 145 15 29 24 114 117 interleaver 170 6 89 78 74 105 21 159 177 162 156 71 input, 63 66 101 98 179 164 111 5 84 36 87 37 95 161 11 133 154 50 47 86 4 137 22 130 134 140 61 42 1 16 131 103 172 129 146 116 70 17 46 59 113 124 176 132 7 73 56 14 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 72 91 30 125 173 109 8 115 82 79 2 block of 26 118 128 144 121 57 41 52 94 110 45 Group-wise 169 12 65 38 19 43 20 23 149 147 108 interleaver 49 80 60 138 157 155 96 143 126 90 93 input, 174 35 160 152 141 127 81 64 67 92 33 148 178 97 88 40 10 9 136 32 123 158 55 76 58 83 166 27 139 163 99 165 53 44 34 31 153 151 142 25

In the case of Table 30, Equation 17 may be expressed as Y₀=X_(π(0))=X₇₇, Y₁=X_(π(1))=X₃₉, Y₂=X_(π(2))=X₃, . . . , Y₁₇₈=X_(π(178))=X₁₄₂, and Y₁₇₉=X_(π(179))=X₂₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 77^(th) bit group to the 0^(th) bit group, the 39^(th) bit group to the 1^(st) bit group, the 3^(rd) bit group to the 2^(nd) bit group, . . . , the 142^(th) bit group to the 178^(th) bit group, and the 25^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 31 presented below.

TABLE 31 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 7 87 5 66 23 42 149 43 148 16 58 9 block of 25 35 41 173 123 167 3 59 81 116 39 72 Group-wise 132 130 164 169 14 71 75 53 98 21 170 127 interleaver 156 115 50 47 112 38 117 69 157 138 120 57 input, 99 83 63 62 133 177 6 19 64 52 103 22 11 160 151 124 158 8 100 105 51 48 67 128 174 152 113 111 107 85 96 49 84 18 131 141 89 95 45 26 56 162 137 165 125 104 92 28 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 82 102 79 12 163 135 147 172 108 93 10 block of 97 159 178 136 155 1 94 109 78 33 2 Group-wise 146 142 54 106 91 118 40 61 179 145 153 interleaver 44 80 0 24 70 139 176 161 122 29 15 input, 73 34 154 140 143 144 65 4 30 36 20 134 17 13 101 90 76 55 27 37 168 126 60 77 88 86 68 114 171 129 175 166 46 119 110 32 31 74 150 121

In the case of Table 31, Equation 17 may be expressed as Y₀=X_(π(0))=X₇, Y₁=X_(π(1))=X₈₇, Y₂=X_(π(2))=X₅, . . . , Y₁₇₈=X_(π(178))=X₁₅₀, and Y₁₇₉=X_(π(179))=X₁₂₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 7^(th) bit group to the 0^(th) bit group, the 87^(th) bit group to the 1^(st) bit group, the 5^(th) bit group to the 2^(nd) bit group, . . . , the 150^(th) bit group to the 178^(th) bit group, and the 121^(st) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 32 presented below.

TABLE 32 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 111 32 70 77 54 93 122 65 165 144 45 101 block of 117 60 42 131 177 148 11 97 23 10 20 114 Group-wise 154 139 163 134 63 68 99 106 105 119 6 167 interleaver 130 15 31 73 102 103 21 142 176 143 146 9 input, 12 113 80 76 136 89 132 145 39 110 1 72 28 162 168 147 129 24 58 61 115 91 34 123 155 125 100 87 90 30 46 86 150 170 149 5 62 14 29 33 92 174 127 158 18 41 85 47 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 95 2 38 7 126 13 156 128 78 82 57 block of 51 160 166 179 175 75 79 50 74 59 40 Group-wise 3 124 35 98 118 83 67 8 22 172 133 interleaver 107 27 109 0 81 141 153 121 161 25 19 input, 64 112 157 152 169 120 94 48 17 88 4 135 173 164 84 71 55 37 66 36 159 52 49 43 56 116 108 69 171 138 178 151 44 26 104 53 137 96 16 140

In the case of Table 32, Equation 17 may be expressed as Y₀=X_(π(0))=X₁₁₁, Y₁=X_(π(1))=X₃₂, Y₂=X_(π(2))=X₇₀, . . . , Y₁₇₈=X_(π(178))=X₁₆, and Y₁₇₉=X_(π(179))=X₁₄₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 111^(th) bit group to the 0^(th) bit group, the 32^(nd) bit group to the 1^(st) bit group, the 70^(th) bit group to the 2^(nd) bit group, . . . , the 16^(th) bit group to the 178^(th) bit group, and the 140^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 33 presented below.

TABLE 33 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 91 88 112 102 26 27 120 103 17 15 19 136 block of 64 98 29 126 164 167 5 106 121 73 86 37 Group-wise 149 54 179 163 40 133 92 39 44 139 74 166 interleaver 175 67 2 48 125 25 109 178 123 160 151 32 input, 110 119 34 59 18 0 161 176 31 38 80 6 142 42 10 156 153 78 69 138 35 128 96 165 24 158 79 81 85 71 84 99 134 162 170 168 58 130 45 28 13 140 66 159 8 95 46 57 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 60 83 116 89 115 72 147 148 11 52 33 block of 62 143 93 174 146 14 1 53 100 55 50 Group-wise 3 172 20 4 75 49 70 56 41 43 173 interleaver 21 47 108 7 77 129 113 155 169 22 122 input, 114 127 131 154 152 150 23 12 76 118 135 63 177 171 68 111 87 61 137 105 101 107 141 82 65 30 51 90 36 157 9 144 117 94 97 124 132 104 16 145

In the case of Table 33, Equation 17 may be expressed as Y₀=X_(π(0))=X₉₁, Y₁=X_(π(1))=X₈₈, Y₂=X_(π(2))=X₁₁₂, . . . , Y₁₇₈=X_(π(178))=X₁₆, and Y₁₇₉=X_(π(179))=X₁₄₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 91^(st) bit group to the 0^(th) bit group, the 88^(th) bit group to the 1^(st) bit group, the 112^(th) bit group to the 2^(nd) bit group, . . . , the 16^(th) bit group to the 178^(th) bit group, and the 145^(th) bit group to the 179^(th) bit group.

In the above-described examples, the length of the LDPC codeword is 64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, this is merely an example and the interleaving pattern may be defined variously when the length of the LDPC codeword is 16200 or the code rate has different values.

As described above, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by using Equation 17 and Tables 29 to 33.

“j-th block of Group-wise Interleaver output” in Tables 29 to 33 indicates the j-th bit group output from the group interleaver 122 after interleaving, and “π(j)-th block of Group-wise Interleaver input” indicates the π(j)-th bit group input to the group interleaver 122.

In addition, since the order of the bit groups constituting the LDPC codeword is rearranged by the group interleaver 122 in bits group wise, and then the bit groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 29 to 33 in relation to π(j).

π(j) defined as shown in Tables 29 to 33 may be arranged according to the code rates as shown in Table 34 presented below:

TABLE 34 (CR 6/15) (CR 8/15) (CR 10/15) (CR 10/15) (CR 12/15) j-th block of π(j)-th block of π(j)-th block of π(j)-th block of π(j)-th block of π(j)-th block of Group-wise Group-wise Group-wise Group-wise Group-wise Group-wise Interleaver Interleaver Interleaver Interleaver Interleaver Interleaver output input input input input input 0 66 77 7 111 91 1 59 39 87 32 88 2 22 3 5 70 112 3 15 175 66 77 102 4 106 102 23 54 26 5 97 62 42 93 27 6 74 119 149 122 120 7 88 0 43 65 103 8 132 171 148 165 17 9 134 104 16 144 15 10 21 48 58 45 19 11 14 13 9 101 136 12 31 72 82 95 60 13 37 91 102 2 83 14 127 30 79 38 116 15 149 125 12 7 89 16 142 173 163 126 115 17 87 109 135 13 72 18 125 8 147 156 147 19 82 115 172 128 148 20 51 82 108 78 11 21 40 79 93 82 52 22 161 2 10 57 33 23 148 68 25 117 64 24 76 112 35 60 98 25 143 28 41 42 29 26 166 168 173 131 126 27 93 167 123 177 164 28 174 106 167 148 167 29 95 135 3 11 5 30 55 51 59 97 106 31 42 75 81 23 121 32 38 54 116 10 73 33 9 85 39 20 86 34 131 122 72 114 37 35 81 26 97 51 62 36 7 118 159 160 143 37 103 128 178 166 93 38 169 144 136 179 174 39 133 121 155 175 146 40 54 57 1 75 14 41 62 41 94 79 1 42 30 52 109 50 53 43 13 94 78 74 100 44 105 110 33 59 55 45 32 45 2 40 50 46 5 120 132 154 149 47 94 107 130 139 54 48 168 150 164 163 179 49 164 100 169 134 163 50 24 69 14 63 40 51 56 18 71 68 133 52 19 145 75 99 92 53 45 15 53 106 39 54 138 29 98 105 44 55 96 24 21 119 139 56 119 114 170 6 74 57 140 117 127 167 166 58 79 169 146 3 3 59 154 12 142 124 172 60 33 65 54 35 20 61 2 38 106 98 4 62 17 19 91 118 75 63 46 43 118 83 49 64 75 20 40 67 70 65 3 23 61 8 56 66 20 149 179 22 41 67 165 147 145 172 43 68 84 108 153 133 173 69 120 170 156 130 175 70 12 6 115 15 67 71 43 89 50 31 2 72 18 78 47 73 48 73 152 74 112 102 125 74 130 105 38 103 25 75 78 21 117 21 109 76 144 159 69 142 178 77 6 177 157 176 123 78 118 162 138 143 160 79 110 156 120 146 151 80 70 71 57 9 32 81 64 49 44 107 21 82 4 80 80 27 47 83 50 60 0 109 108 84 101 138 24 0 7 85 107 157 70 81 77 86 151 155 139 141 129 87 137 96 176 153 113 88 179 143 161 121 155 89 170 126 122 161 169 90 63 90 29 25 22 91 58 93 15 19 122 92 41 63 99 12 110 93 49 66 83 113 119 94 167 101 63 80 34 95 86 98 62 76 59 96 90 179 133 136 18 97 157 164 177 89 0 98 147 111 6 132 161 99 114 5 19 145 176 100 47 84 64 39 31 101 67 36 52 110 38 102 25 87 103 1 80 103 27 37 22 72 6 104 117 174 73 64 114 105 98 35 34 112 127 106 11 160 154 157 131 107 10 152 140 152 154 108 91 141 143 169 152 109 153 127 144 120 150 110 65 81 65 94 23 111 53 64 4 48 12 112 44 67 30 17 76 113 77 92 36 88 118 114 173 33 20 4 135 115 16 95 11 28 142 116 156 161 160 162 42 117 85 11 151 168 10 118 160 133 124 147 156 119 72 154 158 129 153 120 145 50 8 24 78 121 68 47 100 58 69 122 136 86 105 61 138 123 60 4 51 115 35 124 113 137 48 91 128 125 162 22 67 34 96 126 100 130 128 123 165 127 141 148 134 135 63 128 163 178 17 173 177 129 109 97 13 164 171 130 8 88 101 84 68 131 61 40 90 71 111 132 29 10 76 55 87 133 35 9 55 37 61 134 108 136 27 66 137 135 150 32 37 36 105 136 175 123 168 159 101 137 129 158 126 52 107 138 115 134 174 155 24 139 171 140 152 125 158 140 0 61 113 100 79 141 39 42 111 87 81 142 36 1 107 90 85 143 48 16 85 30 71 144 92 131 96 46 84 145 111 103 49 86 99 146 83 172 84 150 134 147 146 129 18 170 162 148 89 146 131 149 170 149 176 116 141 5 168 150 57 55 60 49 141 151 52 76 77 43 82 152 26 58 88 56 65 153 178 83 86 116 30 154 135 166 68 108 51 155 158 27 114 69 90 156 155 139 171 171 36 157 122 163 129 138 157 158 80 99 175 178 9 159 99 165 166 151 144 160 23 53 46 44 117 161 69 70 89 62 58 162 126 17 95 14 130 163 28 46 45 29 45 164 124 59 26 33 28 165 172 113 56 92 13 166 159 124 162 174 140 167 73 176 137 127 66 168 102 132 165 158 159 169 116 7 125 18 8 170 71 73 104 41 95 171 1 56 92 85 46 172 177 14 28 47 57 173 34 44 119 26 94 174 121 34 110 104 97 175 139 31 32 53 124 176 128 153 31 137 132 177 112 151 74 96 104 178 104 142 150 16 16 179 123 25 121 140 145

“j-th block of Group-wise Interleaver output” in Table 34 indicates the j-th bit group output from the group interleaver 122 after interleaving, and “π(j)-th block of Group-wise Interleaver input” indicates the π(j)-th bit group input to the group interleaver 122. Referring to Table 34, it can be seen that Table 34 is the arrangements of data described in Tables 29 to 33 according to the code rates.

The group interleaver 122 may interleave the LDPC codeword in bits group wise by using Equation 18 presented below:

Y _(π(j)) =X _(j)(0≤j<N _(group))  (18),

where X_(j) is the j^(th) bit group before group interleaving, and Y_(j) is the j^(th) bit group after group interleaving. In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate, and a modulation method.

Accordingly, X_(j) is a j^(th) bit group before group interleaving, and Equation 18 means that the pre-interleaving j^(th) bit group is interleaved into the π(j)^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 35 to 39 presented below.

In this case, π(j) is defined according to a length of an LPDC codeword and a code rate, and a parity check matrix is also defined according to a length of an LDPC codeword and a code rate. Accordingly, when LDPC encoding is performed based on a specific parity check matrix according to a length of an LDPC codeword and a code rate, the LDPC codeword may be interleaved in bits group wise based on π(j) satisfying the corresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rate of 6/15 to generate an LDPC codeword of a length of 64800, the group interleaver 122 may perform interleaving by using π(j) which is defined according to the length of the LDPC codeword of 64800 and the code rate of 6/15 in Tables 35 to 39 presented below, for example, by using π(j) defined as shown in Table 35.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 35 presented below.

TABLE 35 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 140 171 61 65 82 46 77 36 130 33 107 106 block of 160 50 102 152 103 163 132 42 12 45 60 173 Group-wise 63 100 143 93 83 20 151 111 40 30 51 150 interleaver 161 80 170 119 167 6 64 24 113 75 58 158 output, 144 27 47 29 55 5 105 159 126 84 168 37 138 169 104 78 56 69 174 157 179 164 18 162 54 175 57 127 16 25 76 120 147 98 23 15 22 125 128 49 67 26 94 48 38 89 139 165 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 70 43 11 3 115 62 72 52 66 10 2 block of 133 142 143 32 141 21 92 31 71 112 53 Group-wise 91 1 123 131 41 90 81 110 0 101 121 interleaver 35 19 146 68 117 95 17 7 148 96 108 output, 178 44 4 85 134 129 79 145 177 124 99 14 176 137 74 34 8 39 9 154 122 87 135 86 73 109 59 156 116 97 155 166 118 114 28 136 149 172 153 88

In the case of Table 35, Equation 18 may be expressed as X₀=Y_(π(0))=Y₁₄₀, X₁=Y_(π(1))=Y₁₇₁, X₂=Y_(π(2))=Y₆₁, . . . , X₁₇₈=Y_(π(178))=Y₁₅₃, and X₁₇₉=Y_(π(179))=Y₈₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 140^(th) bit group, the 1^(st) bit group to the 171^(st) bit group, the 2^(nd) bit group to the 61^(st) bit group, . . . , the 178^(th) bit group to the 153^(rd) bit group, and the 179^(th) bit group to the 88^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 36 presented below.

TABLE 36 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 7 142 22 2 123 99 70 169 18 133 132 117 block of 65 55 179 35 155 25 54 14 175 135 114 174 Group-wise 163 121 10 81 120 30 42 160 32 150 171 40 interleaver 50 161 80 12 170 73 31 151 0 72 21 82 output, 113 91 43 115 87 129 95 158 49 94 4 145 19 149 57 36 6 46 39 34 136 166 15 89 84 156 139 108 178 88 38 52 148 67 127 66 116 78 157 97 159 154 27 26 58 69 8 146 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 59 11 172 53 143 162 51 62 64 75 125 block of 105 101 103 61 1 131 41 141 63 173 45 Group-wise 152 164 83 140 5 92 111 60 93 112 23 interleaver 110 20 153 100 33 122 102 130 71 90 13 output, 9 74 28 47 68 17 44 98 24 165 56 109 37 147 126 144 168 118 138 29 134 124 48 177 107 176 119 86 79 85 137 76 106 16 104 3 167 77 128 98

In the case of Table 36, Equation 18 may be expressed as X₀=Y_(π(0))=Y₇, X₁=Y_(π(1))=Y₁₄₂, X₂=Y_(π(2))=Y₂₂, . . . , X₁₇₈=Y_(π(178))=Y₁₂₈, and X₁₇₉=Y_(π(179))=Y₉₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 7^(th) bit group, the 1^(st) bit group to the 142^(nd) bit group, the 2^(nd) bit group to the 22^(nd) bit group, . . . , the 178^(th) bit group to the 128^(th) bit group, and the 179^(th) bit group to the 98^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 37 presented below.

TABLE 37 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 83 40 45 29 111 2 98 0 120 11 22 115 block of 4 84 23 164 134 172 90 112 176 175 44 105 Group-wise 160 72 124 145 71 123 101 53 60 133 165 80 interleaver 76 85 51 34 104 177 52 132 151 43 14 82 output, 171 21 41 162 144 35 54 92 121 130 13 102 70 32 75 63 173 79 179 89 27 118 169 137 78 86 107 149 59 108 109 67 58 18 8 6 88 166 16 48 168 159 28 136 49 56 156 19 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 15 129 50 91 9 128 147 99 114 55 103 block of 24 113 135 74 33 64 25 5 7 81 163 Group-wise 10 30 150 65 95 94 100 110 3 125 154 interleaver 31 12 93 146 143 153 1 152 161 131 62 output, 170 122 61 142 20 42 174 141 73 140 155 57 126 157 47 148 46 96 127 17 38 167 178 117 139 68 106 39 69 77 119 36 116 26 138 158 87 97 37 66

In the case of Table 37, Equation 18 may be expressed as X₀=Y_(π(0))=Y₈₃, X₁=Y_(π(1))=Y₄₀, X₂=Y_(π(2))=Y₄₅, . . . , X₁₇₈=Y_(π(178))=Y₃₇, and X₁₇₉=Y_(π(179))=Y₆₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 83^(rd) bit group, the 1^(st) bit group to the 40^(th) bit group, the 2^(nd) bit group to the 45^(th) bit group, . . . , the 178^(th) bit group to the 37^(th) bit group, and the 179^(th) bit group to the 66^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 38 presented below.

TABLE 38 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 84 102 13 58 114 149 56 15 65 80 32 29 block of 31 120 90 173 82 115 163 143 71 1 164 125 Group-wise 144 172 111 150 42 35 137 175 4 132 152 22 interleaver 155 2 131 103 72 43 40 95 3 20 41 94 output, 165 5 110 12 177 30 61 52 140 11 73 74 123 153 23 62 55 109 88 6 126 59 139 16 157 47 179 86 76 78 9 99 79 118 28 148 89 116 48 129 8 37 57 117 108 147 156 67 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 92 17 162 70 178 112 169 91 33 75 66 block of 60 135 133 14 100 45 170 25 151 160 10 Group-wise 121 44 24 122 161 50 104 7 134 64 51 interleaver 85 21 63 130 171 145 141 113 97 142 124 output, 174 54 53 81 154 83 101 0 105 93 34 167 19 119 69 26 98 68 49 127 96 176 146 159 107 87 46 138 18 106 168 136 36 128 166 39 77 27 158 38

In the case of Table 38, Equation 18 may be expressed as X₀=Y_(π(0))=Y₈₄, X₁=Y_(π(1))=Y₁₀₂, X₂=Y_(π(2))=Y₁₃, . . . , X₁₇₈=Y_(π(178))=Y₁₅₈, and X₁₇₉=Y_(π(179))=Y₃₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 84^(th) bit group, the 1^(st) bit group to the 102^(th) bit group, the 2^(nd) bit group to the 13^(th) bit group, . . . , the 178^(th) bit group to the 158^(th) bit group, and the 179^(th) bit group to the 38^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 39 presented below.

TABLE 39 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j)-th 97 41 71 58 61 29 103 84 169 158 117 20 block of 110 138 74 4 5 164 25 153 100 80 22 94 Group-wise 171 82 72 63 45 154 21 42 47 44 65 172 interleaver 121 64 143 17 32 56 62 112 85 120 140 102 output, 52 37 173 170 125 174 24 145 43 136 3 7 16 14 160 113 93 6 31 91 77 175 73 26 122 55 166 150 115 36 159 179 39 18 19 46 98 147 49 27 126 57 28 149 89 148 129 59 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 111 165 40 9 178 8 96 10 60 81 90 block of 123 156 34 101 53 50 66 116 67 54 163 Group-wise 161 95 12 133 35 127 23 152 167 70 130 interleaver 141 151 13 144 142 33 132 1 15 155 0 output, 177 135 30 137 83 75 92 131 2 87 104 105 124 86 162 106 176 51 146 114 11 134 109 79 108 119 107 88 118 157 139 168 78 68 38 69 99 128 76 48

In the case of Table 39, Equation 18 may be expressed as X₀=Y_(π(0))=Y₉₇, X₁=Y_(π(1))=Y₄₁, X₂=Y_(π(2))=Y₇₁, . . . , X₁₇₈=Y_(π(178))=Y₇₆, and X₁₇₉=Y_(π(179))=Y₄₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by changing the 0^(th) bit group to the 97^(th) bit group, the 1^(st) bit group to the 41^(st) bit group, the 2^(nd) bit group to the 71^(st) bit group, . . . , the 178^(th) bit group to the 76^(th) bit group, and the 179^(th) bit group to the 48^(th) bit group.

In the above-described examples, the length of the LDPC codeword is 64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, this is merely an example and the interleaving pattern may be defined variously when the length of the LDPC codeword is 16200 or the code rate has different values.

As described above, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by using Equation 18 and Tables 35 to 39.

“j-th block of Group-wise Interleaver input” in Tables 35 to 39 indicates the j-th bit group input to the group interleaver 122 before interleaving, and “π(j)-th block of Group-wise Interleaver output” indicates the π(j)-th bit group output from the group interleaver 122 after interleaving.

In addition, since the order of the bit groups constituting the LDPC codeword is rearranged by the group interleaver 122 in bits group wise, and then the bit groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 35 to 39 in relation to π(j).

π(j) defined as shown in Tables 35 to 39 may be arranged according to the code rates as shown in Table 40:

TABLE 40 (CR 6/15) (CR 8/15) (CR 10/15) (CR 10/15) (CR 12/15) j-th block of □(j)-th block of □(j)-th block of □(j)-th block of □(j)-th block of □(j)-th block of Group-wise Group-wise Group-wise Group-wise Group-wise Group-wise Interleaver Interleaver Interleaver Interleaver Interleaver Interleaver input output output output output output 0 140 7 83 84 97 1 171 142 40 102 41 2 61 22 45 13 71 3 65 2 29 58 58 4 82 123 111 114 61 5 46 99 2 149 29 6 77 70 98 56 103 7 36 169 0 15 84 8 130 18 120 65 169 9 33 133 11 80 158 10 107 132 22 32 117 11 106 117 115 29 20 12 70 59 15 92 111 13 43 11 129 17 165 14 11 172 50 162 40 15 3 53 91 70 9 16 115 143 9 178 178 17 62 162 128 112 8 18 72 51 147 169 96 19 52 62 99 91 10 20 66 64 114 33 60 21 10 75 55 75 81 22 2 125 103 66 90 23 160 65 4 31 110 24 50 55 84 120 138 25 102 179 23 90 74 26 152 35 164 173 4 27 103 155 134 82 5 28 163 25 172 115 164 29 132 54 90 163 25 30 42 14 112 143 153 31 12 175 176 71 100 32 45 135 175 1 80 33 60 114 44 164 22 34 173 174 105 125 94 35 133 105 24 60 123 36 142 101 113 135 156 37 13 103 135 133 34 38 32 61 74 14 101 39 141 1 33 100 53 40 21 131 64 45 50 41 92 41 25 170 66 42 31 141 5 25 116 43 71 63 7 151 67 44 112 173 81 160 54 45 53 45 163 10 163 46 63 163 160 144 171 47 100 121 72 172 82 48 143 10 124 111 72 49 93 81 145 150 63 50 83 120 71 42 45 51 20 30 123 35 154 52 151 42 101 137 21 53 111 160 53 175 42 54 40 32 60 4 47 55 30 150 133 132 44 56 51 171 165 152 65 57 150 40 80 22 172 58 91 152 10 121 161 59 1 164 30 44 95 60 123 83 150 24 12 61 131 140 65 122 133 62 41 5 95 161 35 63 90 92 94 50 127 64 81 111 100 104 23 65 110 60 110 7 152 66 0 93 3 134 167 67 101 112 125 64 70 68 121 23 154 51 130 69 161 50 76 155 121 70 80 161 85 2 64 71 170 80 51 131 143 72 119 12 34 103 17 73 167 170 104 72 32 74 6 73 177 43 56 75 64 31 52 40 62 76 24 151 132 95 112 77 113 0 151 3 85 78 75 72 43 20 120 79 58 21 14 41 140 80 158 82 82 94 102 81 35 110 31 85 141 82 19 20 12 21 151 83 146 153 93 63 13 84 68 100 146 130 144 85 117 33 143 171 142 86 95 122 153 145 33 87 17 102 1 141 132 88 7 130 152 113 1 89 148 71 161 97 15 90 96 90 131 142 155 91 108 13 62 124 0 92 144 113 171 165 52 93 27 91 21 5 37 94 47 43 41 110 173 95 29 115 162 12 170 96 55 87 144 177 125 97 5 129 35 30 174 98 105 95 54 61 24 99 159 158 92 52 145 100 126 49 121 140 43 101 84 94 130 11 136 102 168 4 13 73 3 103 37 145 102 74 7 104 178 9 170 174 177 105 44 74 122 54 135 106 4 28 61 53 30 107 85 47 142 81 137 108 134 68 20 154 83 109 129 17 42 83 75 110 79 44 174 101 92 111 145 98 141 0 131 112 177 24 73 105 2 113 124 165 140 93 87 114 99 56 155 34 104 115 138 19 70 123 16 116 169 149 32 153 14 117 104 57 75 23 160 118 78 36 63 62 113 119 56 6 173 55 93 120 69 46 79 109 6 121 174 39 179 88 31 122 157 34 89 6 91 123 179 136 27 126 77 124 164 166 118 59 175 125 18 15 169 139 73 126 162 89 137 16 26 127 14 109 57 167 105 128 176 37 126 19 124 129 137 147 157 119 86 130 74 126 47 69 162 131 34 144 148 26 106 132 8 168 46 98 176 133 39 118 96 68 51 134 9 138 127 49 146 135 154 29 17 127 114 136 122 134 38 96 11 137 87 124 167 176 134 138 54 84 78 157 122 139 175 156 86 47 55 140 57 139 107 179 166 141 127 108 149 86 150 142 16 178 59 76 115 143 25 88 108 78 36 144 76 38 109 9 159 145 120 52 67 99 179 146 147 148 58 79 39 147 98 67 18 118 18 148 23 127 8 28 19 149 15 66 6 148 46 150 135 48 178 146 109 151 86 177 117 159 79 152 73 107 139 107 108 153 109 176 68 87 119 154 59 119 106 46 107 155 156 86 39 138 88 156 116 79 69 18 118 157 97 85 77 106 157 158 155 137 119 168 139 159 166 76 36 136 168 160 118 106 116 36 78 161 22 116 88 89 98 162 125 78 166 116 147 163 128 157 16 48 49 164 49 97 48 129 27 165 67 159 168 8 126 166 26 154 159 37 57 167 94 27 28 57 28 168 48 26 136 117 149 169 38 58 49 108 89 170 89 69 56 147 148 171 139 8 156 156 129 172 165 146 19 67 59 173 114 16 26 128 68 174 28 104 138 166 38 175 136 3 158 39 69 176 149 167 87 77 99 177 172 77 97 27 128 178 153 128 37 158 76 179 88 96 66 38 48

Table 34 is the case in which group interleaving is performed using Equation 17 and π(j) is applied as an index of an input bit group, and Table 40 is the case in which group interleaving is performed using Equation 18 and π(j) is applied as an index of an output bit group. Therefore, Tables 34 and 40 have an inverse relationship with each other.

As described above, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise by using Equation 18 and Tables 35 to 39.

When the group interleaving is performed in the above-described method, the order of the bit groups constituting the group-interleaved LDPC codeword is different from that of the bit groups of the LDPC codeword group-interleaved based on Tables 9 to 20.

This is because the block-row interleaver 125 is used instead of the block interleaver 124 in the present exemplary embodiment. That is, since the interleaving method used in the block interleaver 124 and the interleaving method used in the block-row interleaver 125 are different from each other, the group interleaver 122 in the present exemplary embodiment may rearrange the order of the plurality of bit groups constituting the LDPC codeword based on Tables 29 to 40.

Specifically, the group interleaver 122 may rearrange the order of the plurality of bit groups in bits group wise such that an arrangement unit, in which at least one bit group including bits to be mapped onto a same modulation symbol is serially arranged in bit group wise, is repeated.

That is, the group interleaver 122 may serially arrange one of a plurality of first bit groups including bits to be mapped onto a first specific location of each modulation symbol, one of a plurality of second bit groups including bits to be mapped onto a second specific location of each modulation symbol, . . . , one of a plurality of n^(th) bit groups including bits to be mapped onto an n^(th) specific location of each modulation symbol, and may arrange the other bit groups repeatedly in the same method.

The block-row interleaver 125 interleaves the plurality of bit groups the order of which has been rearranged. In this case, the block-row interleaver 125 may interleave the plurality of bit groups the order of which has been rearranged in bits group wise by using at least one row including a plurality of columns. This will be explained in detail below with reference to FIGS. 15 to 17.

FIGS. 15 to 17 are views to illustrate a configuration of a block-row interleaver and an interleaving method according to an exemplary embodiment.

First, when N_(group)/m is an integer, the block-row interleaver 125 includes an interleaver 125-1 including m number of rows each including M number of columns as shown in FIG. 15, and the block-row interleaver 125 may interleave by using N_(group)/m number of interleavers 125-1 having the configuration of FIG. 15.

Herein, N_(group) is the total number of bit groups constituting an LDPC codeword. In addition, M is the number of bits included in a single bit group and may be 360, for example. m may be equal to the number of bits constituting a modulation symbol or may be 1/2 of the number of bits constituting a modulation symbol. For example, when a non-uniform QAM is used, performance of the bits constituting the modulation symbol is different, and thus, by setting m to be equal to the number of bits constituting the modulation symbol, a single bit group can be mapped onto a single bit of each modulation symbol.

Specifically, the block-row interleaver 125 may interleave by writing each of the plurality of bit groups constituting the LDPC codeword in each row in the row direction in bits group wise, and reading each column of the plurality of rows in which the plurality of bit groups are written in bit group wise in the column direction.

For example, as shown in FIG. 15, the block-row interleaver 125 may write m number of continuous bit groups from among the plurality of bit groups in each of the m number of rows of the interleaver 125-1 in the row direction, and read each column of m number of rows in which the bits are written in the column direction. In this case, as many interleavers 125-1 as the number of bit groups divided by the number of rows, that is, N_(group)/m, may be used.

As described above, when the number of bit groups constituting the LDPC codeword is an integer multiple of the number of rows, the block-row interleaver 125 may interleave by writing as many bit groups as the number of rows from among the plurality of bit groups serially.

On the other hand, when the number of bit groups constituting the LDPC codeword is not an integer multiple of the number of rows, the block-row interleaver 125 may interleave by using N number of interleavers (N is an integer greater than or equal to 2) including a different number of columns.

For example, as shown in FIGS. 16 and 17, the block-row interleaver 125 may interleave by using a first interleaver 125-2 including m number of rows each including M number of columns, and a second interleaver 125-3 including m number of rows each including a×M/m number of columns. Herein, a is N_(group)−└N_(group)/m┘×m, and └N_(group)/m┘ is the largest integer below N_(group)/m.

In this case, the first interleaver 125-2 may be used as many as └N_(group)/m┘ and one second interleaver 125-3 may be used.

Specifically, the block-row interleaver 125 may interleave by writing each of └N_(group)/m┘×m number of bit groups from among the plurality of bit groups constituting the LDPC codeword in each row in the row direction in bits group wise, and reading each column of the plurality of rows in which └N_(group)/m┘×m number of bit groups are written in bits group wise in the column direction.

For example, as shown in FIGS. 16 and 17, the block-row interleaver 125 may write the same m number of continuous bit groups as the number of rows from among └N_(group)/m┘×M number of bit groups in each row of the first interleaver 125-2 in the row direction, and may read each column of the plurality of rows of the first interleaver 125-2 in which m number of bit groups are written in the column direction. In this case, the first interleaver 125-2 having the configuration FIGS. 16 and 17 may be used as many as └N_(group)/m┘.

Thereafter, the block-row interleaver 125 may divide the bits included in bit groups other than the groups written in the first interleaver 125-2, and may write these bits in each row of the second interleaver 125-3 in the row direction. In this case, the same number of bits may be written in each row of the second interleaver 125-3.

For example, as shown in FIG. 16, the block-row interleaver 125 may write, in each of m number of rows of the second interleaver 125-3, a×M/m number of bits from among the bits included in the other bit groups, in the row direction, and may read each column of m number of rows of the second interleaver 125-3 in which the bits are written in the column direction. In this case, one second interleaver 125-3 having the configuration of FIG. 16 may be used.

However, according to another exemplary embodiment, as shown in FIG. 17, the block-row interleaver 125 may write the bits in the first interleaver 125-2 in the same method as explained in FIG. 16, but may write the bits in the second interleaver 125-3 in a method different from that of FIG. 16.

That is, the block-row interleaver 125 may write the bits in the second interleaver 125-3 in the column direction.

For example, as shown in FIG. 17, the block-row interleaver 125 may write the bits included in the bit groups other than the bit groups written in the first interleaver 125-2 in each column of m number of rows each including a×M/m number of columns of the second interleaver 125-3 in the column direction, and may read each column of m number of rows of the second interleaver 125-3 in which the bits are written in the column direction. In this case, one second interleaver 125-3 having the configuration of FIG. 17 may be used.

In the method shown in FIG. 17, the block-row interleaver 125 may interleave by reading in the column direction after writing the bits in the second interleaver in the column direction. Accordingly, the bits included in the bit groups interleaved by the second interleaver are read in the order as they were written and output to the modulator 130. Accordingly, the bits included in the bit groups belonging to the second interleaver are not rearranged by the block-row interleaver 125 and may be mapped onto the modulation symbols serially.

As described above, the block-row interleaver 125 may interleave the plurality of bit groups by using the methods described above with reference to FIGS. 15 to 17.

According to the above-described method, the output of the block-row interleaver 125 may be the same as the output of the block interleaver 124. Specifically, when the block-row interleaver 125 interleaves as shown in FIG. 15, the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 8. In addition, when the block-row interleaver 125 interleaves as shown in FIG. 16, the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 9. In addition, when the block-row interleaver 125 interleaves as shown in FIG. 17, the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 10.

Specifically, when the group interleaver 122 is used based on Equation 15 and the block interleaver 124 is used, and the output bit groups of the group interleaver 122 are Y_(i)(0≤j<N_(group)) and, when the group interleaver 122 is used based on Equation 17 and the block-row interleaver 125 is used, and the output groups of the group interleaver 122 are Z_(i)(0≤j<N_(group)) a relationship between the output bit groups Z_(i) and Y_(i) after group interleaving may be expressed as in Equations 19 and 20, and as a result, the same value may be output from the block interleaver 124:

Z _(i+m×j) =Y _(α×i+j)(0≤i<m,0≤j<α)  (19)

Z _(i) =Y _(i)(α×m≤i<N _(group))  (20)

where a is └N_(group)/m┘ and is the number of bit groups input to a single column of the first part when the block interleaver 124 is used, and └N_(group)/m┘ is the largest integer below N_(group)/m. Here, m may be equal to the number of bits constituting the modulation symbol or half of the bits constituting the modulation symbol. In addition, m is the number of columns of the block interleaver 124 and m is the number of rows of the block-row interleaver 125.

The case in which group interleaving is performed by the group interleaver 122 based on Equation 15 and then block interleaving is performed by the block interleaver 124, and the case in which group interleaving is performed by the group interleaver 122 based on Equation 16 and then block interleaving is performed by the block interleaver 124 have an inverse relationship with each other.

In addition, the case in which group interleaving is performed by the group interleaver 122 based on Equation 17 and then block-row interleaving is performed by the block-row interleaver 125, and the case in which group interleaving is performed by the group interleaver 122 based on Equation 18 and then block-row interleaving is performed by the block-row interleaver 125 have an inverse relationship with each other.

Accordingly, the modulator 130 may map the bits output from the block-row interleaver 125 onto a modulation symbol in the same method as when the block interleaver 124 is used.

The bit interleaving method suggested in the exemplary embodiments is performed by the parity interleaver 121, the group interleaver 122, the group twist interleaver 123, and the block interleaver 124 as shown in FIG. 4 (the group twist interleaver 123 may be omitted according to circumstances). However, this is merely an example and the bit interleaving method is not limited to three modules or four modules described above.

For example, when the block interleaver is used and the group interleaving method expressed as in Equation 11 is used, regarding the bit groups X_(j)(0≤j<N_(group)) defined as in Equation 9 and Equation 10, bits belonging to m number of bit groups, for example, {X_(π(i)), X_(π(α+i)), . . . , X_(π((m−1)×α+i))} (0≤i<α), may constitute a single modulation symbol.

Herein, α is the number of bit groups constituting the first part of the block interleaver, and α=└N_(group)/m┘. In addition, m is the number of columns of the block interleaver and may be equal to the number of bits constituting the modulation symbol or half of the number of bits constituting the modulation symbol.

Therefore, for example, regarding parity-interleaved bits u_(i), {u_(π(i)+j), u_(π(α+i)+j), . . . , u_(π((m−1)×α+i)+)} (0<i≤m, 0<j≤M) may constitute a single modulation symbol. As described above, there are various methods for constituting a single modulation symbol.

In addition, the bit interleaving method suggested in the exemplary embodiments is performed by the parity interleaver 121, the group interleaver 122, the group twist interleaver 123, and the block-row interleaver 125 as shown in FIG. 14 (the group twist interleaver 123 may be omitted according to circumstances). However, this is merely an example and the bit interleaving method is not limited to three modules or four modules described above.

For example, when the block-row interleaver is used and the group interleaving method expressed as in Equation 17 is used, regarding the bit groups X_(j)(0≤j<N_(group)) defined as in Equation 13 and Equation 14, bits belonging to m number of bit groups, for example, {X_(π(m×i)), X_(π(m×i+1)), . . . , X_(π(m×i+(m−1)))} (0≤i<α), may constitute a single modulation symbol.

Herein, a is the number of bit groups constituting the first part of the block interleaver, and α=└N_(group)/m┘. In addition, m is the number of columns of the block interleaver and may be equal to the number of bits constituting the modulation symbol or half of the number of bits constituting the modulation symbol.

Therefore, for example, regarding parity-interleaved bits u_(i), {u_(π(m×i)+j), u_(π(m×i+1)+j), . . . , u_(π(m×i+(m−1))+j)} (0<i≤m, 0<j≤M) may constitute a single modulation symbol. As described above, there are various methods for constituting a single modulation symbol.

The transmitting apparatus 100 may transmit the signal mapped onto the constellation to a receiving apparatus 2700. For example, the transmitting apparatus 100 may map the signal mapped onto the constellation onto an Orthogonal Frequency Division Multiplexing (OFDM) frame using OFDM, and may transmit the signal to the receiving apparatus 2700 through an allocated channel.

FIG. 18 is a block diagram to illustrate a configuration of a receiving apparatus according to an exemplary embodiment. Referring to FIG. 18, the receiving apparatus 2700 includes a demodulator 2710, a multiplexer 2720, a deinterleaver 2730 and a decoder 2740.

The demodulator 2710 receives and demodulates a signal transmitted from the transmitting apparatus 100. Specifically, the demodulator 2710 generates a value corresponding to an LDPC codeword by demodulating the received signal, and outputs the value to the multiplexer 2720. In this case, the demodulator 2710 may use a demodulation method corresponding to a modulation method used in the transmitting apparatus 100. To do so, the transmitting apparatus 100 may transmit information regarding the modulation method to the receiving apparatus 2700, or the transmitting apparatus 100 may perform modulation using a pre-defined modulation method between the transmitting apparatus 100 and the receiving apparatus 2700.

The value corresponding to the LDPC codeword may be expressed as a channel value for the received signal. There are various methods for determining the channel value, and for example, a method for determining a Log Likelihood Ratio (LLR) value may be the method for determining the channel value.

The LLR value is a log value for a ratio of the probability that a bit transmitted from the transmitting apparatus 100 is 0 and the probability that the bit is 1. In addition, the LLR value may be a bit value which is determined by a hard decision, or may be a representative value which is determined according to a section to which the probability that the bit transmitted from the transmitting apparatus 100 is 0 or 1 belongs.

The multiplexer 2720 multiplexes the output value of the demodulator 2710 and outputs the value to the deinterleaver 2730.

Specifically, the multiplexer 2720 is an element corresponding to a demultiplexer (not shown) provided in the transmitting apparatus 100, and performs an operation corresponding to the demultiplexer (not shown). However, when the demultiplexer (not shown) is omitted from the transmitting apparatus 100, the multiplexer 2720 may be omitted from the receiving apparatus 2700.

That is, the multiplexer 2720 performs an inverse operation of the operation of the demultiplexer (not shown), and performs cell-to-bit conversion with respect to the output value of the demodulator 2710 and outputs the LLR value in the unit of bit.

In this case, when the demultiplexer (not shown) does not change the order of the LDPC codeword bits, the multiplexer 2720 may output the LLR values serially in the unit of bit without changing the order of the LLR values corresponding to the bits of the cell. Alternatively, the multiplexer 2720 may rearrange the order of the LLR values corresponding to the bits of the cell to perform an inverse operation to the demultiplexing operation of the demultiplexer (not shown) based on Table 27.

The information regarding whether the demultiplexing operation is performed or not may be provided by the transmitting apparatus 100, or may be pre-defined between the transmitting apparatus 100 and the receiving apparatus 2700.

The deinterleaver 2730 deinterleaves the output value of the multiplexer 2720 and outputs the values to the decoder 2740.

Specifically, the deinterleaver 2730 is an element corresponding to the interleaver 120 of the transmitting apparatus 100 and performs an operation corresponding to the interleaver 120. That is, the deinterleaver 2730 deinterleaves the LLR value by performing the interleaving operation of the interleaver 120 inversely.

In this case, the deinterleaver 2730 may include elements as shown in FIG. 19 or 21.

First, as shown in FIG. 19, the deinterleaver 2730 may include a block deinterleaver 2731, a group twist deinterleaver 2732, a group deinterleaver 2733, and a parity deinterleaver 2734.

The block deinterleaver 2731 deinterleaves the output of the multiplexer 2720 and outputs the value to the group twist deinterleaver 2732.

Specifically, the block deinterleaver 2731 is an element corresponding to the block interleaver 124 provided in the transmitting apparatus 100 and performs the interleaving operation of the block interleaver 124 inversely.

That is, the block deinterleaver 2731 may deinterleave by using at least one row formed of a plurality of columns, that is, by writing the LLR value output from the multiplexer 2720 in each row in the row direction and reading each column of the plurality of rows in which the LLR value is written in the column direction.

In this case, when the block interleaver 124 interleaves by dividing a column into two parts, the block deinterleaver 2731 may deinterleave by dividing a row into two parts.

In addition, when the block interleaver 124 performs writing and reading with respect to a bit group which does not belong to the first part in the row direction, the block deinterleaver 2731 may deinterleave by writing and reading a value corresponding to the group which does not belong to the first part in the row direction.

Hereinafter, the block deinterleaver 2731 will be explained with reference to FIG. 20. However, this is merely an example and the block deinterleaver 2731 may be implemented in other methods.

An input LLR v_(i) (0≤i<N_(ldpc)) is written in a r_(i) row and a c_(i) column of the block deinterleaver 2431. Herein, c_(i)=(i mod N_(c)) and

${r_{i} = \left\lfloor \frac{i}{N_{c}} \right\rfloor},$

On the other hand, an output LLR q_(i)(0≤i<N_(c)×N_(r1)) is read from a c_(i) column and a r_(i) row of the first part of the block deinterleaver 2431. Herein,

${c_{i} = \left\lfloor \frac{i}{N_{r1}} \right\rfloor},$

r_(i)=(i mod N_(r1)).

In addition, an output LLR q_(i)(N_(c)×N_(r1)≤i<N_(ldpc)) is read from a c_(i) column and a r_(i) row of the second part. Herein,

${c_{i} = \left\lfloor \frac{\left( {i - {N_{c} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor},$

r_(i)=N_(r1)+{(i−N_(c)×N_(r1)) mode N_(r2)}.

The group twist deinterleaver 2732 deinterleaves the output value of the block deinterleaver 2731 and outputs the value to the group deinterleaver 2733.

Specifically, the group twist deinterleaver 2732 is an element corresponding to the group twist interleaver 123 provided in the transmitting apparatus 100, and may perform the interleaving operation of the group twist interleaver 123 inversely.

That is, the group twist deinterleaver 2732 may rearrange the LLR values of the same group by changing the order of the LLR values existing in the same group. When the group twist operation is not performed in the transmitting apparatus 100, the group twist deinterleaver 2732 may be omitted.

The group deinterleaver 2733 (or the group-wise deinterleaver) deinterleaves the output value of the group twist deinterleaver 2732 and outputs the value to the parity deinterleaver 2734.

Specifically, the group deinterleaver 2733 is an element corresponding to the group interleaver 122 provided in the transmitting apparatus 100 and may perform the interleaving operation of the group interleaver 122 inversely.

That is, the group deinterleaver 2733 may rearrange the order of the plurality of bit groups in bits group wise. In this case, the group deinterleaver 2733 may rearrange the order of the plurality of bit groups in bits group wise by applying the interleaving method of Tables 9 to 20 inversely according to a length of the LDPC codeword, a modulation method and a code rate.

The parity deinterleaver 2734 performs parity deinterleaving with respect to the output value of the group deinterleaver 2733 and outputs the value to the decoder 2740.

Specifically, the parity deinterleaver 2734 is an element corresponding to the parity interleaver 121 provided in the transmitting apparatus 100 and may perform the interleaving operation of the parity interleaver 121 inversely. That is, the parity deinterleaver 2734 may deinterleave the LLR values corresponding to the parity bits from among the LLR values output from the group deinterleaver 2733. In this case, the parity deinterleaver 2734 may deinterleave the LLR values corresponding to the parity bits in an inverse method of the parity interleaving method of Equation 8.

However, the parity deinterleaver 2734 may be omitted according to the decoding method and implementation of the decoder 2740.

The deinterleaver 2730 may include a block-row deinterleaver 2735, a group twist deinterleaver 2732, a group deinterleaver 2733 and a parity deinterleaver 2734, as shown in FIG. 21. In this case, the group twist deinterleaver 2732 and the parity deinterleaver 2734 perform the same functions as in FIG. 19, and thus, a redundant explanation is omitted.

The block-row deinterleaver 2735 deinterleaves the output value of the multiplexer 2720 and outputs the value to the group twist deinterleaver 2732.

Specifically, the block-row deinterleaver 2735 is an element corresponding to the block-row interleaver 125 provided in the transmitting apparatus 100 and may perform the interleaving operation of the block-row interleaver 125 inversely.

That is, the block-row deinterleaver 2735 may deinterleave by using at least one column formed of a plurality of rows, that is, by writing the LLR values output from the multiplexer 2720 in each column in the column direction and reading each row of the plurality of columns in which the LLR value is written in the column direction.

However, when the block-row interleaver 125 performs writing and reading with respect to a bit group which does not belong to the first part in the column direction, the block-row deinterleaver 2735 may deinterleave by writing and reading a value corresponding to the bit group which does not belong to the first part in the column direction.

The group deinterleaver 2733 deinterleaves the output value of the group twist deinterleaver 2732 and outputs the value to the parity deinterleaver 2734.

Specifically, the group deinterleaver 2733 is an element corresponding to the group interleaver 122 provided in the transmitting apparatus 100 and may perform the interleaving operation of the group interleaver 122 inversely.

That is, the group deinterleaver 2733 may rearrange the order of the plurality of bit groups in bit group wise. In this case, the group deinterleaver 2733 may rearrange the order of the plurality of bit groups in bits group wise by applying the interleaving method of Tables 29 to 40 inversely according to a length of the LDPC codeword, a modulation method and a code rate.

Although the deinterleaver 2730 of FIG. 18 includes three (3) or four (4) elements as shown in FIG. 19 or 21, operations of the elements may be performed by a single element. For example, when bits each of which belongs to each of bit groups X_(a), X_(b), X_(c), X_(d), X_(e), X_(f), X_(g), X_(h), X_(i), X_(j) constitute a single modulation symbol, the deinterleaver 2730 may deinterleave these bits to locations corresponding to their bit groups based on the received single modulation symbol.

For example, when the code rate is 6/15 and the modulation method is 1024-QAM, the group deinterleaver 2733 may perform deinterleaving based on Table 9.

In this case, bits each of which belongs to each of bit groups X₆₆, X₅₉, X₂₂, X₁₅, X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, X₁₃₄ constitute a single modulation symbol. Since one bit in each of the bit groups X₆₆, X₅₉, X₂₂, X₁₅, X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, X₁₃₄ constitutes a single modulation symbol, the deinterleaver 2730 may map bits onto decoding initial values corresponding to the bit groups X₆₆, X₅₉, X₂₂, X₁₅, X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, X₁₃₄ based on the received single modulation symbol.

The decoder 2740 may perform LDPC decoding by using the output value of the deinterleaver 2730. To achieve this, the decoder 2740 may include an LDPC decoder (not shown) to perform the LDPC decoding.

Specifically, the decoder 2740 is an element corresponding to the encoder 110 of the transmitting apparatus 100 and may correct an error by performing the LDPC decoding by using the LLR value output from the deinterleaver 2730.

For example, the decoder 2740 may perform the LDPC decoding in an iterative decoding method based on a sum-product algorithm. The sum-product algorithm is one example of a message passing algorithm, and the message passing algorithm refers to an algorithm which exchanges messages (e.g., LLR value) through an edge on a bipartite graph, calculates an output message from messages input to variable nodes or check nodes, and updates.

The decoder 2740 may use a parity check matrix when performing the LDPC decoding. In this case, an information word submatrix in the parity check matrix is defined as in Tables 4 to 20 according to a code rate and a length of the LDPC codeword, and a parity submatrix may have a dual diagonal configuration.

In addition, information on the parity check matrix and information on the code rate, etc. which are used in the LDPC decoding may be pre-stored in the receiving apparatus 2700 or may be provided by the transmitting apparatus 100.

FIG. 22 is a flowchart to illustrate an interleaving method of a transmitting apparatus according to an exemplary embodiment.

First, an LDPC codeword is generated by LDPC encoding based on a parity check matrix (S3010). In this case, in the LDPC encoding, a parity check matrix in which an information word submatrix is defined by Tables 4 to 8 and a parity submatrix has a dual diagonal configuration (that is, the parity check matrix of FIG. 2) may be used, or a parity check matrix which is row and column permutated from the parity check matrix of FIG. 2 based on Equations 4 and 5 (that is, the configuration of FIG. 3) may be used.

Thereafter, the LDPC codeword is interleaved (S3020).

Then, the interleaved LDPC codeword is mapped onto a modulation symbol (S3030). In this case, bits included in a predetermined number of bit groups from among the plurality of bit groups of the LDPC codeword may be mapped onto a predetermined bit of a modulation symbol.

In this case, each of the plurality of bit groups may be formed of M number of bits, and M may be a common divisor of N_(ldpc) and K_(ldpc) and may be determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Herein, Q_(ldpc) is a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, N_(ldpc) is a length of the LDPC codeword, and K_(ldpc) is a length of information word bits of the LDPC codeword.

Operation S3020 may include interleaving parity bits of the LDPC codeword, dividing the parity-interleaved LDPC codeword by the plurality of bit groups and rearranging the order of the plurality of bit groups in bits group wise, and interleaving the plurality of bit groups the order of which has been rearranged.

Specifically, the order of the plurality of bit groups may be rearranged in bits group wise based on the above-described Equation 15 presented above. In Equation 15, π(j) is determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

For example, when the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 6/15, π(j) may be defined as in Table 9 presented above.

In another example, when the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 8/15, π(j) may be defined as in Table 10 presented above.

In another example, when the LDPC codeword has a length of 64800, the modulation method is 1024-QAM, and the code rate is 12/15, π(j) may be defined as in Table 13 presented above.

However, this is merely an example. π(j) may be defined as in Tables 11 or 12 described above.

In addition, Equation 16 may be used in rearranging the order of the plurality of bit groups in bits group wise. In this case, π(j) may be defined as in Tables 15 to 20 described above.

The plurality of bit groups the order of which has been rearranged may be interleaved by writing the plurality of bit groups in each of the plurality of columns in the column direction in bit group wise, and reading each row of the plurality of columns in which the plurality of bit groups are written in bits group wise in the row direction.

In this case, from among the plurality of bit groups, at least some bit group which can be written in each of the plurality of columns in bits group wise is written in each of the plurality of columns serially, and then, the other bit groups are divided and written in the other areas which remain in each of the plurality of columns after the at least some bit group has been written in bits group wise.

In operation S3020, the interleaving may be performed in other methods in addition to the above-described method.

Specifically, the interleaving may be performed by using Equation 17 and Tables 29 to 34 described above, or may be performed by using Equation 18 and Tables 35 to 40 described above.

In these cases, the order of the plurality of bit groups may be rearranged in bits group wise such that an arrangement unit, in which at least one bit groups including bits to be mapped onto the same modulation symbol is serially arranged in bits group units, is repeated.

When a plurality of bit groups are interleaved, the interleaving may be performed by writing, in each row, at least one bit group including bits to be mapped onto a same modulation symbol from among the plurality of bit groups the order of which has been rearranged, in the row direction, and reading each column of the row in which the at least one bit group is written in the column direction.

A non-transitory computer readable medium, which stores a program for performing the interleaving methods according to various exemplary embodiments in sequence, may be provided. The non-transitory computer readable medium refers to a medium that stores data semi-permanently rather than storing data for a very short time, such as a register, a cache, and a memory, and is readable by an apparatus. Specifically, the above-described various applications or programs may be stored in a non-transitory computer readable medium such as a compact disc (CD), a digital versatile disk (DVD), a hard disk, a Blu-ray disk, a universal serial bus (USB), a memory card, and a read only memory (ROM), and may be provided.

At least one of the components, elements or units represented by a block as illustrated in FIGS. 1, 4, 13, 14, 18, 19 and 21 may be embodied as various numbers of hardware, software and/or firmware structures that execute respective functions described above, according to an exemplary embodiment. For example, at least one of these components, elements or units may use a direct circuit structure, such as a memory, processing, logic, a look-up table, etc. that may execute the respective functions through controls of one or more microprocessors or other control apparatuses. Also, at least one of these components, elements or units may be specifically embodied by a module, a program, or a part of code, which contains one or more executable instructions for performing specified logic functions. Also, at least one of these components, elements or units may further include a processor such as a central processing unit (CPU) that performs the respective functions, a microprocessor, or the like. Two or more of these components, elements or units may be combined into one single component, element or unit which performs all operations or functions of the combined two or more components, elements of units. Further, although a bus is not illustrated in the above block diagrams, communication between the components, elements or units may be performed through the bus. Functional aspects of the above exemplary embodiments may be implemented in algorithms that execute on one or more processors. Furthermore, the components, elements or units represented by a block or processing steps may employ any number of related art techniques for electronics configuration, signal processing and/or control, data processing and the like.

Although a bus is not illustrated in the block diagrams of the transmitting apparatus and the receiving apparatus, communication may be performed between each element of each apparatus via the bus. In addition, each apparatus may further include a processor such as a Central Processing Unit (CPU) or a microprocessor to perform the above-described various operations.

The foregoing exemplary embodiments and advantages are merely exemplary and are not to be construed as limiting the present inventive concept. The exemplary embodiments can be readily applied to other types of apparatuses. Also, the description of the exemplary embodiments is intended to be illustrative, and not to limit the scope of the inventive concept, and many alternatives, modifications, and variations will be apparent to those skilled in the art. 

What is claimed is:
 1. A receiving method comprising: demodulating a signal received from a transmitting apparatus to generate values based on 1024-quadrature amplitude modulation (QAM); splitting the values into a plurality of groups; deinterleaving the plurality of groups based on an interleaving order; and decoding values of the deinterleaved plurality of groups based on a low density parity check (LDPC) code, a code rate of the LDPC code being 6/15 and a code length of the LDPC code being 64800, wherein the plurality of groups are deinterleaved based on a following equation: Y _(π(j)) =X _(j) for (0≤j<N _(group)), where X_(j) is a j-th group among the plurality of groups, Y_(j) is a j-th group among the deinterleaved plurality of groups, N_(group) is a number of the plurality of groups, and π(j) denotes the interleaving order, and wherein the π(j) is represented as follows: Code Rate Order of the interleaving 6/15 π(j) (0 ≤ j < 180) j 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j) 66 21 51 55 54 24 33 12 70 63 47 65 56 2 43 64 58 67 53 68 61 39 52 69 25 44 136 29 36 26 126 177 15 37 148 9 178 28 34 106 127 76 131 105 138 75 130 101 143 81 32 96 3 78 107 86 98 16 162 150 144 151 90 11 156 100 175 83 155 159 128 88 141 129 146 122 73 112 132 125 174 169 168 79 104 134 82 95 133 164 154 120 110 170 114 153 Code Rate Order of the interleaving 6/15 π(j) (0 ≤ j < 180) j 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j) 145 8 0 57 23 71 59 14 40 42 62 1 22 31 161 38 30 19 17 18 4 41 13 45 46 152 50 49 27 77 60 35 48 167 117 173 113 108 92 135 124 121 97 149 111 158 172 139 74 142 166 7 5 119 20 87 93 103 94 140 165 6 137 157 10 85 84 118 179 147 91 160 163 115 89 80 102 72 109 171 176 99 116 123


2. The receiving method of claim 1, wherein each of the plurality of groups comprises 360 values. 